CompositeInterpolationXTable-internal.hpp

/*
 * Licensed to the Apache Software Foundation (ASF) under one
 * or more contributor license agreements.  See the NOTICE file
 * distributed with this work for additional information
 * regarding copyright ownership.  The ASF 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.
 */
 
#ifndef _COMPOSITEINTERPOLATIONXTABLE_INTERNAL_HPP_
#define _COMPOSITEINTERPOLATIONXTABLE_INTERNAL_HPP_
 
#include "HllUtil.hpp"
#include "CompositeInterpolationXTable.hpp"
 
#include <exception>
#include <stdexcept>
 
namespace datasketches {
 
static const uint32_t numXArrValues = 257;
 
static const uint32_t yStrides[] =
  {1, 2, 3, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920};
 
template<typename A>
uint32_t CompositeInterpolationXTable<A>::get_y_stride(uint8_t logK) {
  if (logK < hll_constants::MIN_LOG_K || logK > hll_constants::MAX_LOG_K) {
    throw std::invalid_argument("logK must be in range [" + std::to_string(hll_constants::MIN_LOG_K)
                                + ", " + std::to_string(hll_constants::MAX_LOG_K) + "]. Found: "
                                + std::to_string(logK));
  }
  return yStrides[logK - hll_constants::MIN_LOG_K];
}
 
template<typename A>
uint32_t CompositeInterpolationXTable<A>::get_x_arr_length() {
  return numXArrValues;
}
 
static const double xArray[18][numXArrValues] = {
{
  10.767999803534, 11.237701481774, 11.722738717438, 12.223246391222,
  12.739366773787, 13.271184824495, 13.818759686650, 14.382159835785,
  14.961390904922, 15.556414447178, 16.167227058768, 16.793705840034,
  17.435831011559, 18.093368824077, 18.766214022468, 19.454114555153,
  20.156877376380, 20.874309118151, 21.606085061388, 22.351926834624,
  23.111406651437, 23.884222842419, 24.669953053285, 25.468324695415,
  26.278740385032, 27.100807701976, 27.934264623663, 28.778498012717,
  29.633064579479, 30.497559091830, 31.371415928956, 32.254248998304,
  33.145649456017, 34.045084140394, 34.952069032314, 35.866210502243,
  36.787128772113, 37.714316067007, 38.647432342061, 39.586020708848,
  40.529738186256, 41.478377527525, 42.431435504179, 43.388619067416,
  44.349650659292, 45.314111448463, 46.281805382722, 47.252472240229,
  48.225969481651, 49.202042512440, 50.180350422249, 51.160761480664,
  52.143032445587, 53.127233235412, 54.112986437616, 55.100182392694,
  56.088558030701, 57.078156023607, 58.068788167275, 59.060493030644,
  60.053033784417, 61.046284072738, 62.040286486621, 63.034929032992,
  64.030027371399, 65.025588917110, 66.021614945599, 67.018177418440,
  68.015186786528, 69.012467972526, 70.010014322660, 71.007638150468,
  72.005472777573, 73.003558069130, 74.001925061314, 75.000323809106,
  75.998875046818, 76.997735309722, 77.996356820987, 78.995236661037,
  79.994185446564, 80.993179953574, 81.991936172868, 82.991277726952,
  83.990564675011, 84.990016215330, 85.989354175963, 86.988664031183,
  87.988038383374, 88.987487931153, 89.987011275632, 90.986376635228,
  91.985802667485, 92.985125933965, 93.984894049744, 94.984597185523,
  95.984374633793, 96.983987641198, 97.983728001025, 98.983151114601,
  99.982917278162, 100.982752268263, 101.982610588914, 102.982425129077,
  103.982425883214, 104.982193814993, 105.982188025268, 106.982005912713,
  107.981949640254, 108.981777381902, 109.981767708570, 110.981785341504,
  111.981686149156, 112.981635012054, 113.981557303839, 114.981412817204,
  115.981636136290, 116.981451847734, 117.981619278961, 118.981656205677,
  119.981462628717, 120.981648197593, 121.981672839888, 122.981536601882,
  123.981424780957, 124.981245233627, 125.981297203177, 126.981469882453,
  127.981420558510, 128.981470958251, 129.981803124940, 130.981454077005,
  131.981307772677, 132.981136552712, 133.981060440468, 134.980764897921,
  135.980250123519, 136.979947889981, 137.979778713731, 138.979651075854,
  139.979521006237, 140.979619490143, 141.979418214464, 142.979378742690,
  143.979006714929, 144.978789085341, 145.978940618746, 146.978699584620,
  147.978509489139, 148.978375065557, 149.978382007245, 150.978320879037,
  151.978431501891, 152.978357310224, 153.978079953131, 154.977867908315,
  155.977897282267, 156.977732141540, 157.977285841428, 158.977381755450,
  159.977107808858, 160.976898092463, 161.976945065052, 162.976415653211,
  163.976063254486, 164.976168718176, 165.976009634854, 166.975746910144,
  167.975365498336, 168.975302031315, 169.975145815395, 170.975048401084,
  171.974904933990, 172.974962856090, 173.974307743427, 174.974505556696,
  175.974404122880, 176.974154794798, 177.973936891006, 178.973909768514,
  179.973629325330, 180.973396428571, 181.973041798012, 182.972922327014,
  183.972453839631, 184.972389341638, 185.971978290400, 186.971721489488,
  187.971610992921, 188.971432541974, 189.970886522529, 190.970636748690,
  191.970543849249, 192.970222044828, 193.969945219163, 194.969816174441,
  195.969660267113, 196.969306217626, 197.969283141670, 198.968952697752,
  199.968650726389, 200.968771498143, 201.969063388798, 202.968624157712,
  203.968385122471, 204.968459873029, 205.968253426841, 206.968128284823,
  207.968002441937, 208.967981887571, 209.967853843352, 210.967653026858,
  211.967601511385, 212.967479077297, 213.967293002672, 214.967265475369,
  215.967098197208, 216.966915139758, 217.966680984700, 218.966156974161,
  219.965788928685, 220.965578199561, 221.965550145047, 222.965055562297,
  223.965041228123, 224.965088576052, 225.964951649635, 226.964837079061,
  227.964949815142, 228.964753278386, 229.964358666956, 230.964158288467,
  231.964118659643, 232.964105599719, 233.964013041408, 234.963810178150,
  235.963847138572, 236.963634735645, 237.963596910032, 238.963659218725,
  239.963498440155, 240.963445597658, 241.963141291971, 242.962684055746,
  243.962664757583, 244.962762174588, 245.962862664373, 246.962595237647,
  247.962493432533, 248.962292518484, 249.962622934132, 250.962187495200,
  251.962038306920, 252.961926735684, 253.961867248643, 254.961699581530,
  255.961371028199
},
// log K = 5
{
  22.304000309384, 23.261989079230, 24.249656493833, 25.267226901899,
  26.314781734430, 27.392414068382, 28.500177845081, 29.638044883897,
  30.805888087516, 32.003714838418, 33.231360682863, 34.488477823483,
  35.774924122967, 37.090293268866, 38.434292452116, 39.806594197334,
  41.206691028159, 42.634002763091, 44.088065403269, 45.568286128520,
  47.074066947685, 48.604745105475, 50.159729872619, 51.738339282229,
  53.339805618020, 54.963435280656, 56.608464119077, 58.274038434156,
  59.959403900602, 61.663926660982, 63.386737477574, 65.127093833107,
  66.884091606686, 68.656959698762, 70.445052178435, 72.247581860591,
  74.063607663774, 75.892531705810, 77.733879994604, 79.586788509372,
  81.450593478752, 83.324645303244, 85.208482496209, 87.101116685537,
  89.002152917959, 90.911090999940, 92.827275073114, 94.750224301260,
  96.679773715696, 98.615214511699, 100.556211548644, 102.502148428334,
  104.452899214344, 106.407767504404, 108.366625832228, 110.329564692634,
  112.295481742874, 114.264715056639, 116.236769512562, 118.211214593179,
  120.188376370012, 122.167746134232, 124.148833002551, 126.131612799989,
  128.116072530208, 130.102155735854, 132.089449244974, 134.077816832908,
  136.067404409248, 138.057703527432, 140.049350564796, 142.041756984355,
  144.034780624078, 146.028584459531, 148.022894428003, 150.017952482368,
  152.013358245376, 154.009157360372, 156.005076955043, 158.001501688538,
  159.998043891849, 161.995141096448, 163.992507770330, 165.990019741406,
  167.987379363144, 169.985323168231, 171.983371903769, 173.981134136378,
  175.979306888599, 177.977458741010, 179.975994045101, 181.974478508488,
  183.973329438036, 185.972061903815, 187.971014174496, 189.969582278901,
  191.968450510061, 193.967607022497, 195.966726931677, 197.965915341472,
  199.964910588293, 201.964427852336, 203.964308576556, 205.963778587196,
  207.963244179225, 209.962423156859, 211.961859295409, 213.961171237132,
  215.960624048009, 217.959980906604, 219.959156277574, 221.958692298143,
  223.958335010302, 225.958329061602, 227.957722024027, 229.957134954397,
  231.956897929205, 233.956901572571, 235.956650770311, 237.956593290745,
  239.956700470895, 241.956192761863, 243.956003327600, 245.955794901574,
  247.955501305446, 249.954960233132, 251.954510187803, 253.954252376340,
  255.954011943050, 257.953388008439, 259.953139524693, 261.952918466928,
  263.952432910213, 265.952485387126, 267.952763908808, 269.952510701682,
  271.952383356830, 273.951921008979, 275.951766755515, 277.951697578478,
  279.951700548755, 281.951805228218, 283.951934023417, 285.952140722678,
  287.952063941231, 289.951717207670, 291.951294241955, 293.950937111819,
  295.950900506385, 297.950320403388, 299.949546547128, 301.949474819234,
  303.949155377395, 305.948725010033, 307.948408553357, 309.948120512731,
  311.947897212148, 313.947738181662, 315.947255247579, 317.946631669691,
  319.946302193308, 321.945855881155, 323.945603079048, 325.944930145876,
  327.945048538923, 329.944795565500, 331.944227346318, 333.943705422222,
  335.943231918970, 337.942333069602, 339.942354997227, 341.941890952026,
  343.941346276351, 345.940653575739, 347.940019001109, 349.940026817951,
  351.938944534275, 353.938172407151, 355.937584534690, 357.937041224148,
  359.936673631279, 361.936179855216, 363.936105840596, 365.935367434940,
  367.935295315770, 369.934793960370, 371.934314961518, 373.933949277377,
  375.933420587284, 377.933148188654, 379.932379363314, 381.931900192237,
  383.930951130857, 385.930667541762, 387.930025971711, 389.929529183966,
  391.929116798157, 393.928361940635, 395.927673611921, 397.927111110912,
  399.926483516685, 401.925799510661, 403.924918492428, 405.924540208915,
  407.924014467935, 409.923779779206, 411.922979548363, 413.922515268061,
  415.922148908645, 417.921643066153, 419.921126587639, 421.920766647684,
  423.920642824255, 425.920411492484, 427.920603679205, 429.920445437023,
  431.920286509746, 433.919789058392, 435.919408587813, 437.918873200300,
  439.918417416574, 441.918192491069, 443.918376503567, 445.917692006023,
  447.917132642691, 449.917217997363, 451.916924115487, 453.916662151474,
  455.916485288107, 457.915879851633, 459.915842501592, 461.915547354915,
  463.914995141359, 465.914585759187, 467.914144928428, 469.913956069337,
  471.913046082896, 473.912468624617, 475.912322983182, 477.912118100240,
  479.911923664773, 481.911518944025, 483.911023761757, 485.910386539830,
  487.910092345284, 489.910153786770, 491.909575245360, 493.908973823502,
  495.908577061168, 497.908550221055, 499.908127020659, 501.907710605296,
  503.907806972566, 505.907336571662, 507.907081330259, 509.906648846180,
  511.906201574892
},
// log K = 6
{
  45.375999854524, 46.820948326168, 48.298703712049, 49.809402685314,
  51.353165756275, 52.929933710602, 54.539893242468, 56.183033892089,
  57.859217068495, 59.568519998303, 61.310801009963, 63.085886926328,
  64.893798324934, 66.734230191052, 68.607173306372, 70.512210309984,
  72.449265953981, 74.418007054647, 76.417910710559, 78.448929349152,
  80.510585932256, 82.602514696500, 84.724061528721, 86.875166381330,
  89.055217833675, 91.263852803721, 93.500342620773, 95.764451518395,
  98.055566319691, 100.373234086043, 102.716794393386, 105.085599217566,
  107.479363461004, 109.897282858060, 112.338907676111, 114.803401103124,
  117.290259931022, 119.799265623507, 122.329323908482, 124.879681624600,
  127.450299022993, 130.040239267142, 132.648756733593, 135.275366525219,
  137.919720233989, 140.580778017562, 143.258128898839, 145.951552244700,
  148.660145472460, 151.383257444852, 154.120434694643, 156.871202914301,
  159.634634288797, 162.410377522877, 165.198249005575, 167.997420145534,
  170.807579918337, 173.628020587905, 176.458633641294, 179.298282098581,
  182.147449731726, 185.005094444186, 187.870899328937, 190.744709255561,
  193.625572419776, 196.513740460772, 199.408599560293, 202.309940032246,
  205.217132295894, 208.129828601313, 211.047995735211, 213.970919426104,
  216.899109829571, 219.832024990852, 222.769136305806, 225.710258431247,
  228.655217514772, 231.603984417526, 234.555642012353, 237.510635882749,
  240.468820458907, 243.429903849174, 246.393192036307, 249.359251612075,
  252.327416912482, 255.297598046767, 258.269777722144, 261.244337060733,
  264.219958654591, 267.197643910088, 270.177202282129, 273.157339433786,
  276.139287129066, 279.122276848731, 282.107226383752, 285.092136000673,
  288.078230550129, 291.065256815999, 294.053160971001, 297.042401030971,
  300.031784889467, 303.022502412860, 306.013581138287, 309.005124942334,
  311.996910583050, 314.989635544162, 317.982189300799, 320.975762085573,
  323.969719809182, 326.963672522149, 329.958419674913, 332.953046205989,
  335.948338966110, 338.943201657934, 341.938798787180, 344.935321901459,
  347.931089897905, 350.927355153871, 353.923731760523, 356.920383399325,
  359.916863372939, 362.914245241722, 365.911216314347, 368.908636150615,
  371.905028432797, 374.901981729273, 377.899718967915, 380.897391911925,
  383.894945428721, 386.892974193389, 389.890517424427, 392.889050804732,
  395.886893560179, 398.884852345719, 401.883235933616, 404.881805247652,
  407.880049402262, 410.878410789472, 413.876755787854, 416.875140105536,
  419.873758096660, 422.872739431833, 425.871627898739, 428.870663138631,
  431.869475472357, 434.868378059774, 437.867537661532, 440.866274620049,
  443.865086570094, 446.864282236320, 449.863630871851, 452.862772062678,
  455.861877807413, 458.860680461949, 461.859728874700, 464.858478829514,
  467.857314559298, 470.856707830759, 473.855641079729, 476.854880576501,
  479.853812351976, 482.852666825246, 485.851471230749, 488.850997731659,
  491.850420535006, 494.849118717584, 497.848645341646, 500.848230362352,
  503.847546143645, 506.847285358235, 509.846275998715, 512.845599444922,
  515.845441684852, 518.844522015985, 521.843923976006, 524.843281639782,
  527.842399994830, 530.841152548296, 533.840788827465, 536.840058715879,
  539.839578267778, 542.839076801367, 545.838441853502, 548.837925005355,
  551.837456112430, 554.837041819817, 557.836916936797, 560.836116071833,
  563.834832988710, 566.834107840572, 569.832763471368, 572.831700689757,
  575.832050680783, 578.831190216307, 581.831249402778, 584.830325442080,
  587.828993643112, 590.827962761832, 593.827454067745, 596.825833598259,
  599.824193205007, 602.822806340644, 605.822276069352, 608.821423024191,
  611.820006110523, 614.819016304854, 617.818220240160, 620.817311827644,
  623.816286470744, 626.815211383752, 629.815077535810, 632.813925717940,
  635.813392704099, 638.812424935595, 641.811289306882, 644.809932622788,
  647.808609610738, 650.807771758015, 653.806851303878, 656.805452367508,
  659.804133900742, 662.803103749985, 665.801910649522, 668.800969589926,
  671.798796938405, 674.798110719805, 677.797843657187, 680.797711918663,
  683.796449689643, 686.794998006462, 689.794205385109, 692.792836542916,
  695.792195299304, 698.790778974184, 701.790704644168, 704.790168225574,
  707.789261680438, 710.788674453657, 713.787207421297, 716.786043303658,
  719.784740017888, 722.783523691482, 725.782739693893, 728.781695938105,
  731.780295310459, 734.778719103047, 737.778056368816, 740.777014963309,
  743.776470087777, 746.774710218241, 749.773897180146, 752.772555359445,
  755.771799417720, 758.770328749569, 761.768940347768, 764.768630836408,
  767.767399121425
},
// log K = 7
{
  91.554623, 93.970317, 96.431113, 98.937264, 101.488909, 104.086010, 106.728780, 109.417062,
  112.150914, 114.930279, 117.755065, 120.625143, 123.540431, 126.500927, 129.506371, 132.556551,
  135.651450, 138.790477, 141.973357, 145.200176, 148.470504, 151.783478, 155.139376, 158.537455,
  161.977357, 165.458477, 168.980630, 172.543258, 176.145951, 179.788203, 183.469266, 187.188166,
  190.945533, 194.739618, 198.570460, 202.437447, 206.339379, 210.276276, 214.247092, 218.251243,
  222.288169, 226.357728, 230.458810, 234.590263, 238.751826, 242.942859, 247.162518, 251.410098,
  255.685517, 259.987202, 264.314569, 268.667458, 273.044873, 277.445418, 281.869296, 286.316796,
  290.785471, 295.276055, 299.788143, 304.319743, 308.869691, 313.438842, 318.026761, 322.632499,
  327.254588, 331.892954, 336.547483, 341.217702, 345.901880, 350.601214, 355.313731, 360.038868,
  364.777348, 369.526476, 374.288795, 379.061811, 383.846122, 388.640850, 393.446218, 398.260691,
  403.084626, 407.916053, 412.755659, 417.604951, 422.461448, 427.324128, 432.195028, 437.072269,
  441.956190, 446.846167, 451.741463, 456.641868, 461.549478, 466.461280, 471.377098, 476.297446,
  481.222717, 486.151860, 491.085033, 496.022133, 500.962856, 505.906586, 510.853868, 515.802981,
  520.755460, 525.711123, 530.668833, 535.629910, 540.592334, 545.557764, 550.525455, 555.494082,
  560.463996, 565.436164, 570.410847, 575.385933, 580.361996, 585.339352, 590.318151, 595.300216,
  600.281543, 605.264482, 610.250114, 615.236608, 620.222025, 625.208433, 630.195367, 635.183997,
  640.172271, 645.162589, 650.153647, 655.144276, 660.133923, 665.123818, 670.115789, 675.109169,
  680.103270, 685.097349, 690.091960, 695.086028, 700.080326, 705.075670, 710.069697, 715.065265,
  720.062426, 725.058529, 730.054916, 735.050560, 740.048508, 745.044790, 750.041067, 755.037833,
  760.035090, 765.033371, 770.029865, 775.025946, 780.022408, 785.021534, 790.018699, 795.016742,
  800.013947, 805.012680, 810.009483, 815.007921, 820.008589, 825.007658, 830.007411, 835.006892,
  840.006917, 845.006362, 850.004606, 855.003367, 860.001219, 864.999491, 869.999131, 874.998190,
  879.998460, 884.997482, 889.995952, 894.995130, 899.994555, 904.993474, 909.991434, 914.990519,
  919.991564, 924.992234, 929.993901, 934.992310, 939.992013, 944.993341, 949.993576, 954.992981,
  959.993548, 964.993781, 969.993129, 974.994050, 979.994706, 984.994372, 989.994395, 994.995339,
  999.995544, 1004.995498, 1009.996864, 1014.997829, 1019.996531, 1024.996724, 1029.997574, 1034.998591,
  1039.997807, 1044.998954, 1050.000113, 1055.000633, 1060.000845, 1065.000760, 1070.000907, 1075.001248,
  1080.001187, 1084.999775, 1089.999105, 1094.999647, 1100.001983, 1105.003468, 1110.004542, 1115.005170,
  1120.006517, 1125.006493, 1130.006837, 1135.008369, 1140.006966, 1145.009225, 1150.008497, 1155.009589,
  1160.009558, 1165.011395, 1170.009739, 1175.011131, 1180.013303, 1185.012525, 1190.014190, 1195.016399,
  1200.016087, 1205.016715, 1210.018008, 1215.018108, 1220.019677, 1225.020269, 1230.019468, 1235.020515,
  1240.021850, 1245.020961, 1250.019785, 1255.020253, 1260.020623, 1265.020156, 1270.020625, 1275.019028,
  1280.019972
},
// log K = 8
{
  183.877784, 188.720097, 193.652407, 198.675131, 203.788397, 208.992238, 214.286620, 219.671580,
  225.147277, 230.713559, 236.370208, 242.117078, 247.953569, 253.880078, 259.895869, 266.000405,
  272.193694, 278.474457, 284.843102, 291.298228, 297.839692, 304.466434, 311.177471, 317.972674,
  324.850719, 331.811076, 338.852902, 345.974709, 353.175880, 360.455237, 367.811613, 375.244484,
  382.752472, 390.334218, 397.988777, 405.714596, 413.510671, 421.376147, 429.308973, 437.308197,
  445.372302, 453.500121, 461.690796, 469.942249, 478.253652, 486.623402, 495.049662, 503.532193,
  512.068670, 520.658371, 529.299186, 537.990886, 546.732097, 555.520093, 564.355935, 573.235689,
  582.159345, 591.126063, 600.133321, 609.181348, 618.267848, 627.392384, 636.552822, 645.748152,
  654.977601, 664.239902, 673.534497, 682.859448, 692.213983, 701.598606, 711.009376, 720.446781,
  729.910995, 739.397888, 748.908546, 758.443812, 768.000572, 777.577584, 787.174815, 796.791250,
  806.427107, 816.079660, 825.748493, 835.435992, 845.136828, 854.854141, 864.583886, 874.328396,
  884.085720, 893.855568, 903.637568, 913.431080, 923.234553, 933.049830, 942.873895, 952.707793,
  962.551743, 972.402421, 982.263001, 992.131464, 1002.006941, 1011.888460, 1021.777462, 1031.671376,
  1041.569600, 1051.476632, 1061.386996, 1071.302834, 1081.224251, 1091.148847, 1101.080297, 1111.013589,
  1120.951962, 1130.893360, 1140.838011, 1150.786112, 1160.737100, 1170.689817, 1180.646908, 1190.604979,
  1200.565150, 1210.527894, 1220.492169, 1230.460128, 1240.429764, 1250.401749, 1260.373274, 1270.349608,
  1280.325544, 1290.302087, 1300.279074, 1310.257850, 1320.238948, 1330.221273, 1340.203554, 1350.186669,
  1360.171345, 1370.156233, 1380.142561, 1390.129535, 1400.119177, 1410.107938, 1420.097171, 1430.087586,
  1440.077831, 1450.067996, 1460.060299, 1470.050059, 1480.042995, 1490.035101, 1500.026878, 1510.021128,
  1520.014262, 1530.008487, 1540.002895, 1549.996342, 1559.991075, 1569.986665, 1579.981202, 1589.976021,
  1599.969512, 1609.964051, 1619.959210, 1629.957092, 1639.953516, 1649.948113, 1659.946715, 1669.945253,
  1679.941736, 1689.938651, 1699.937600, 1709.936396, 1719.933608, 1729.931040, 1739.930316, 1749.927141,
  1759.922600, 1769.920847, 1779.918614, 1789.915707, 1799.913000, 1809.910958, 1819.908532, 1829.906905,
  1839.903410, 1849.904217, 1859.901705, 1869.898815, 1879.898869, 1889.899032, 1899.899113, 1909.896164,
  1919.893199, 1929.894515, 1939.894965, 1949.893184, 1959.892164, 1969.890794, 1979.889035, 1989.888005,
  1999.888538, 2009.888252, 2019.888976, 2029.890242, 2039.890655, 2049.891065, 2059.891068, 2069.889204,
  2079.891120, 2089.892462, 2099.892479, 2109.891814, 2119.893049, 2129.893705, 2139.893471, 2149.894162,
  2159.894213, 2169.895041, 2179.895987, 2189.894721, 2199.894028, 2209.896005, 2219.898683, 2229.898673,
  2239.898012, 2249.898018, 2259.898215, 2269.899380, 2279.902590, 2289.903144, 2299.902047, 2309.904214,
  2319.903812, 2329.904180, 2339.902528, 2349.903057, 2359.903089, 2369.904512, 2379.902563, 2389.905522,
  2399.903653, 2409.902313, 2419.904452, 2429.905949, 2439.905059, 2449.904954, 2459.904977, 2469.905111,
  2479.904049, 2489.903762, 2499.902022, 2509.904352, 2519.903272, 2529.901643, 2539.900789, 2549.903045,
  2559.904334
},
// log K = 9
{
  368.528954, 378.224619, 388.100156, 398.155846, 408.391912, 418.808631, 429.406377, 440.185048,
  451.144613, 462.284693, 473.604932, 485.105306, 496.784844, 508.643147, 520.679581, 532.893098,
  545.282616, 557.848295, 570.587645, 583.500268, 596.584345, 609.838697, 623.261582, 636.851681,
  650.607666, 664.527320, 678.608336, 692.849674, 707.248088, 721.803089, 736.511331, 751.372034,
  766.381798, 781.538178, 796.839808, 812.283881, 827.867995, 843.588520, 859.444318, 875.432109,
  891.550599, 907.795630, 924.165943, 940.657393, 957.268601, 973.995685, 990.837235, 1007.789667,
  1024.850025, 1042.016602, 1059.286426, 1076.658199, 1094.126523, 1111.689346, 1129.345589, 1147.092119,
  1164.926795, 1182.844471, 1200.846880, 1218.929006, 1237.088281, 1255.322930, 1273.630393, 1292.007269,
  1310.452948, 1328.963430, 1347.538768, 1366.176566, 1384.871299, 1403.626249, 1422.434094, 1441.295238,
  1460.208340, 1479.169853, 1498.179265, 1517.234855, 1536.335403, 1555.477305, 1574.659180, 1593.881592,
  1613.139378, 1632.433516, 1651.764587, 1671.127255, 1690.519577, 1709.942250, 1729.393153, 1748.871689,
  1768.377142, 1787.907209, 1807.464755, 1827.043146, 1846.641976, 1866.263022, 1885.903553, 1905.564908,
  1925.240581, 1944.936723, 1964.648221, 1984.375489, 2004.117246, 2023.875053, 2043.644075, 2063.423514,
  2083.218689, 2103.026148, 2122.840475, 2142.669046, 2162.505619, 2182.351758, 2202.205963, 2222.068658,
  2241.939010, 2261.814547, 2281.701803, 2301.591894, 2321.490728, 2341.393208, 2361.298412, 2381.211528,
  2401.132345, 2421.057721, 2440.985510, 2460.916691, 2480.851468, 2500.792645, 2520.738446, 2540.683395,
  2560.634603, 2580.586307, 2600.540530, 2620.497170, 2640.458137, 2660.421783, 2680.386186, 2700.352664,
  2720.321411, 2740.291944, 2760.264068, 2780.238910, 2800.212546, 2820.185829, 2840.163952, 2860.142145,
  2880.120568, 2900.102466, 2920.081981, 2940.062964, 2960.046262, 2980.029101, 3000.012591, 3019.998424,
  3039.983637, 3059.969573, 3079.955927, 3099.942114, 3119.930348, 3139.919614, 3159.909130, 3179.899816,
  3199.892231, 3219.885316, 3239.878917, 3259.871675, 3279.865195, 3299.856210, 3319.848871, 3339.840385,
  3359.834158, 3379.830660, 3399.826361, 3419.822855, 3439.814714, 3459.813765, 3479.808673, 3499.804339,
  3519.797785, 3539.791012, 3559.789885, 3579.785152, 3599.780237, 3619.775480, 3639.772724, 3659.768920,
  3679.765735, 3699.766361, 3719.765048, 3739.762845, 3759.761526, 3779.757598, 3799.755719, 3819.751149,
  3839.750182, 3859.749673, 3879.749344, 3899.749939, 3919.749060, 3939.748385, 3959.750520, 3979.750055,
  3999.750104, 4019.749963, 4039.748453, 4059.746737, 4079.744522, 4099.744430, 4119.741804, 4139.740704,
  4159.742056, 4179.740063, 4199.739155, 4219.741718, 4239.743433, 4259.743115, 4279.743265, 4299.745518,
  4319.746682, 4339.750491, 4359.748549, 4379.747226, 4399.750319, 4419.750379, 4439.752339, 4459.750561,
  4479.750612, 4499.747862, 4519.750693, 4539.747476, 4559.749051, 4579.750603, 4599.750089, 4619.754781,
  4639.755536, 4659.758879, 4679.762145, 4699.762199, 4719.763886, 4739.765081, 4759.765681, 4779.765427,
  4799.767582, 4819.769915, 4839.770107, 4859.769398, 4879.768976, 4899.768288, 4919.768786, 4939.768607,
  4959.772822, 4979.772833, 4999.775808, 5019.773468, 5039.776181, 5059.770860, 5079.773006, 5099.773136,
  5119.772474
},
// log K = 10
{
  737.833738, 757.236338, 776.997875, 797.119465, 817.602058, 838.445349, 859.650320, 881.216437,
  903.143414, 925.430957, 948.079220, 971.086231, 994.451449, 1018.173846, 1042.251928, 1066.683804,
  1091.467648, 1116.601416, 1142.083017, 1167.909918, 1194.079097, 1220.588887, 1247.435099, 1274.614860,
  1302.125360, 1329.962942, 1358.123177, 1386.601609, 1415.396299, 1444.501692, 1473.913256, 1503.628515,
  1533.642054, 1563.948888, 1594.544067, 1625.424305, 1656.582169, 1688.016543, 1719.718553, 1751.685990,
  1783.912130, 1816.393610, 1849.122123, 1882.095124, 1915.305647, 1948.748605, 1982.419843, 2016.313904,
  2050.422277, 2084.742618, 2119.270601, 2153.998538, 2188.920843, 2224.034736, 2259.333960, 2294.812594,
  2330.467059, 2366.291844, 2402.281356, 2438.428954, 2474.734330, 2511.187839, 2547.786319, 2584.527356,
  2621.406814, 2658.418551, 2695.554270, 2732.812564, 2770.190157, 2807.682744, 2845.287138, 2882.995251,
  2920.807982, 2958.719996, 2996.728771, 3034.826885, 3073.014082, 3111.287116, 3149.642093, 3188.073159,
  3226.577352, 3265.156836, 3303.803738, 3342.515111, 3381.291514, 3420.130671, 3459.024315, 3497.974631,
  3536.978221, 3576.034737, 3615.138610, 3654.285859, 3693.480455, 3732.715296, 3771.991792, 3811.305300,
  3850.654870, 3890.041152, 3929.457167, 3968.905021, 4008.381466, 4047.886976, 4087.419414, 4126.978997,
  4166.562624, 4206.166726, 4245.793284, 4285.445151, 4325.113012, 4364.802795, 4404.506274, 4444.228475,
  4483.965191, 4523.719569, 4563.487708, 4603.267460, 4643.060387, 4682.865430, 4722.680718, 4762.503248,
  4802.341326, 4842.185529, 4882.039088, 4921.900432, 4961.772625, 5001.649566, 5041.534380, 5081.425809,
  5121.323013, 5161.224908, 5201.130560, 5241.044625, 5280.962456, 5320.882373, 5360.810007, 5400.740058,
  5440.673843, 5480.606748, 5520.547394, 5560.493520, 5600.438100, 5640.383853, 5680.335386, 5720.292400,
  5760.250576, 5800.212705, 5840.172984, 5880.134991, 5920.097923, 5960.060294, 6000.031177, 6040.003398,
  6079.981696, 6119.954349, 6159.929074, 6199.908569, 6239.886163, 6279.863659, 6319.838261, 6359.815405,
  6399.795170, 6439.777225, 6479.755885, 6519.738857, 6559.723169, 6599.708549, 6639.695186, 6679.679788,
  6719.663289, 6759.651052, 6799.634129, 6839.624763, 6879.615013, 6919.605584, 6959.591310, 6999.586006,
  7039.577399, 7079.565236, 7119.557222, 7159.548481, 7199.533025, 7239.519648, 7279.511781, 7319.507639,
  7359.506105, 7399.497488, 7439.494944, 7479.491545, 7519.488415, 7559.480534, 7599.475646, 7639.470315,
  7679.468730, 7719.460928, 7759.455834, 7799.455686, 7839.451758, 7879.446841, 7919.443884, 7959.444138,
  7999.443141, 8039.446339, 8079.445285, 8119.444120, 8159.443157, 8199.446480, 8239.438893, 8279.437597,
  8319.439714, 8359.441566, 8399.440754, 8439.439156, 8479.440112, 8519.442365, 8559.444795, 8599.444497,
  8639.446714, 8679.449177, 8719.447620, 8759.443423, 8799.445995, 8839.446170, 8879.449622, 8919.450486,
  8959.450372, 8999.449731, 9039.448449, 9079.452579, 9119.451596, 9159.454020, 9199.456651, 9239.460902,
  9279.460419, 9319.461322, 9359.464611, 9399.467790, 9439.471448, 9479.468426, 9519.462982, 9559.464881,
  9599.462983, 9639.461706, 9679.457284, 9719.457023, 9759.455648, 9799.458786, 9839.456980, 9879.457411,
  9919.454971, 9959.451735, 9999.451916, 10039.443939, 10079.435325, 10119.432142, 10159.431313, 10199.431306,
  10239.429671
},
// log K = 11
{
  1476.444530, 1515.260638, 1554.794859, 1595.048761, 1636.023652, 1677.720065, 1720.138513, 1763.279158,
  1807.141823, 1851.724811, 1897.027530, 1943.048153, 1989.784818, 2037.234835, 2085.395149, 2134.263580,
  2183.834818, 2234.105548, 2285.071077, 2336.726064, 2389.065940, 2442.084276, 2495.776521, 2550.134177,
  2605.153465, 2660.825522, 2717.142881, 2774.098631, 2831.683790, 2889.889911, 2948.711233, 3008.137464,
  3068.158605, 3128.766926, 3189.951984, 3251.704129, 3314.013826, 3376.873018, 3440.270569, 3504.194851,
  3568.636295, 3633.586039, 3699.031630, 3764.962925, 3831.371336, 3898.245744, 3965.574384, 4033.345701,
  4101.550888, 4170.180686, 4239.221393, 4308.664143, 4378.497100, 4448.712735, 4519.296212, 4590.243535,
  4661.538747, 4733.174738, 4805.142002, 4877.427081, 4950.019513, 5022.915001, 5096.098561, 5169.567185,
  5243.312012, 5317.314578, 5391.572253, 5466.077564, 5540.821377, 5615.792025, 5690.985894, 5766.392174,
  5842.007403, 5917.816734, 5993.815607, 6069.999957, 6146.362662, 6222.895187, 6299.592875, 6376.440778,
  6453.443173, 6530.588182, 6607.874560, 6685.288536, 6762.829840, 6840.490840, 6918.272948, 6996.164556,
  7074.161694, 7152.259404, 7230.451098, 7308.737035, 7387.113244, 7465.575350, 7544.120230, 7622.733447,
  7701.427750, 7780.188044, 7859.016102, 7937.904850, 8016.853624, 8095.860379, 8174.919884, 8254.034842,
  8333.197794, 8412.405307, 8491.657429, 8570.946804, 8650.278289, 8729.648657, 8809.056098, 8888.496764,
  8967.966663, 9047.466051, 9126.993636, 9206.547289, 9286.127523, 9365.733732, 9445.361201, 9525.008810,
  9604.680107, 9684.363532, 9764.066435, 9843.787987, 9923.523567, 10003.272886, 10083.037524, 10162.811803,
  10242.597755, 10322.402415, 10402.216522, 10482.042584, 10561.877077, 10641.722187, 10721.570740, 10801.435848,
  10881.301249, 10961.178474, 11041.059765, 11120.951444, 11200.845806, 11280.746075, 11360.652145, 11440.567398,
  11520.476709, 11600.395391, 11680.316855, 11760.241900, 11840.170134, 11920.103548, 12000.038206, 12079.975425,
  12159.912459, 12239.857191, 12319.802744, 12399.754385, 12479.707055, 12559.658981, 12639.614004, 12719.566502,
  12799.526877, 12879.488833, 12959.451231, 13039.416480, 13119.388158, 13199.360789, 13279.334923, 13359.298927,
  13439.261641, 13519.235871, 13599.204919, 13679.181082, 13759.157391, 13839.137425, 13919.112545, 13999.096522,
  14079.082789, 14159.060487, 14239.040581, 14319.025236, 14399.006995, 14478.994078, 14558.980576, 14638.962774,
  14718.952192, 14798.938522, 14878.931501, 14958.919062, 15038.907891, 15118.897247, 15198.889129, 15278.881057,
  15358.873272, 15438.867627, 15518.861931, 15598.858206, 15678.850014, 15758.849382, 15838.847872, 15918.837658,
  15998.837920, 16078.831305, 16158.827345, 16238.815546, 16318.817302, 16398.814389, 16478.815820, 16558.811634,
  16638.808126, 16718.807170, 16798.805652, 16878.813389, 16958.806543, 17038.807885, 17118.813146, 17198.813752,
  17278.817574, 17358.820511, 17438.819443, 17518.814262, 17598.815511, 17678.814160, 17758.816726, 17838.817584,
  17918.814197, 17998.821276, 18078.822342, 18158.828474, 18238.822064, 18318.826732, 18398.827758, 18478.827319,
  18558.834153, 18638.835651, 18718.839105, 18798.840903, 18878.836463, 18958.836015, 19038.836351, 19118.832583,
  19198.829856, 19278.822953, 19358.824866, 19438.823697, 19518.826538, 19598.826954, 19678.831393, 19758.822279,
  19838.818757, 19918.808247, 19998.804516, 20078.809201, 20158.808900, 20238.806398, 20318.798516, 20398.802224,
  20478.803179
},
// log K = 12
{
  2953.666722, 3031.310137, 3110.389526, 3190.908699, 3272.865410, 3356.267166, 3441.114376, 3527.404284,
  3615.136846, 3704.310976, 3794.924283, 3886.973846, 3980.451903, 4075.355844, 4171.681168, 4269.423939,
  4368.569738, 4469.111760, 4571.043603, 4674.356370, 4779.038117, 4885.076002, 4992.460659, 5101.176875,
  5211.214098, 5322.553631, 5435.184633, 5549.088369, 5664.258175, 5780.673987, 5898.312682, 6017.158593,
  6137.195815, 6258.397951, 6380.761679, 6504.261630, 6628.870413, 6754.585867, 6881.374325, 7009.206926,
  7138.080376, 7267.979175, 7398.866805, 7530.722851, 7663.531580, 7797.269872, 7931.907340, 8067.451667,
  8203.855692, 8341.091306, 8479.155031, 8618.026003, 8757.682272, 8898.095612, 9039.253787, 9181.124777,
  9323.694329, 9466.944202, 9610.861899, 9755.403639, 9900.578346, 10046.356477, 10192.718770, 10339.635914,
  10487.081762, 10635.066232, 10783.560130, 10932.549371, 11082.024055, 11231.949071, 11382.332885, 11533.122831,
  11684.327555, 11835.935533, 11987.926999, 12140.281619, 12292.994375, 12446.046449, 12599.411083, 12753.088314,
  12907.079745, 13061.355923, 13215.895621, 13370.722085, 13525.795736, 13681.095971, 13836.645692, 13992.405906,
  14148.380716, 14304.566860, 14460.959382, 14617.539754, 14774.296125, 14931.214508, 15088.271748, 15245.493870,
  15402.867309, 15560.380994, 15718.035423, 15875.801492, 16033.687891, 16191.701231, 16349.808763, 16508.026001,
  16666.336068, 16824.745049, 16983.259302, 17141.848044, 17300.504517, 17459.240272, 17618.060296, 17776.914688,
  17935.848010, 18094.852645, 18253.914288, 18413.023567, 18572.168358, 18731.376016, 18890.631505, 19049.948196,
  19209.279260, 19368.638871, 19528.043860, 19687.498901, 19846.941765, 20006.443084, 20165.973535, 20325.525957,
  20485.109520, 20644.729917, 20804.363876, 20964.021778, 21123.698687, 21283.379344, 21443.080536, 21602.821439,
  21762.568135, 21922.305338, 22082.065878, 22241.856145, 22401.629436, 22561.435266, 22721.262644, 22881.080478,
  23040.916036, 23200.734053, 23360.583255, 23520.433188, 23680.275065, 23840.132678, 24000.012847, 24159.886135,
  24319.788338, 24479.654024, 24639.540316, 24799.466449, 24959.369335, 25119.276072, 25279.186502, 25439.091982,
  25599.020083, 25758.930671, 25918.847522, 26078.773060, 26238.704021, 26398.647566, 26558.603366, 26718.539855,
  26878.464425, 27038.402892, 27198.344989, 27358.270906, 27518.203448, 27678.169545, 27838.133625, 27998.111630,
  28158.064264, 28318.032491, 28477.994153, 28637.950838, 28797.910362, 28957.884994, 29117.861910, 29277.814384,
  29437.774223, 29597.762256, 29757.729819, 29917.688497, 30077.675371, 30237.667941, 30397.639431, 30557.644527,
  30717.622991, 30877.622641, 31037.598941, 31197.601527, 31357.599118, 31517.585221, 31677.569983, 31837.556138,
  31997.527880, 32157.500622, 32317.491709, 32477.504936, 32637.501123, 32797.516330, 32957.547336, 33117.541765,
  33277.561207, 33437.554332, 33597.564988, 33757.565321, 33917.561180, 34077.580598, 34237.597132, 34397.598246,
  34557.617536, 34717.623318, 34877.649722, 35037.645029, 35197.681143, 35357.700478, 35517.701804, 35677.734383,
  35837.736494, 35997.737103, 36157.732045, 36317.741539, 36477.735602, 36637.761491, 36797.742508, 36957.734137,
  37117.742952, 37277.789218, 37437.793798, 37597.779066, 37757.796449, 37917.794116, 38077.804399, 38237.797507,
  38397.788049, 38557.768583, 38717.768279, 38877.752553, 39037.747349, 39197.737646, 39357.774395, 39517.752643,
  39677.753347, 39837.740038, 39997.719486, 40157.709578, 40317.708657, 40477.719261, 40637.726978, 40797.711139,
  40957.707784
},
// log K = 13
{
  5908.111420, 6063.410343, 6221.578483, 6382.623803, 6546.553966, 6713.369171, 6883.070010, 7055.656719,
  7231.129758, 7409.486672, 7590.720089, 7774.822139, 7961.786850, 8151.601206, 8344.261218, 8539.750086,
  8738.048786, 8939.141702, 9143.011205, 9349.645220, 9559.003557, 9771.078383, 9985.846791, 10203.277103,
  10423.349219, 10646.031323, 10871.293001, 11099.111735, 11329.434411, 11562.255804, 11797.522109, 12035.204106,
  12275.263649, 12517.670237, 12762.388671, 13009.375491, 13258.587519, 13510.006825, 13763.564399, 14019.227089,
  14276.975295, 14536.745792, 14798.511796, 15062.215057, 15327.806593, 15595.257499, 15864.529774, 16135.586770,
  16408.362074, 16682.849583, 16958.977019, 17236.708221, 17515.990972, 17796.798914, 18079.096585, 18362.834517,
  18647.959152, 18934.452073, 19222.251998, 19511.366053, 19801.717928, 20093.269020, 20385.960319, 20679.772736,
  20974.698498, 21270.684814, 21567.671010, 21865.649193, 22164.581341, 22464.423293, 22765.172894, 23066.785452,
  23369.201089, 23672.387494, 23976.354000, 24281.072155, 24586.465328, 24892.557323, 25199.303712, 25506.654130,
  25814.626835, 26123.148009, 26432.247046, 26741.889610, 27052.042135, 27362.685181, 27673.761784, 27985.292246,
  28297.219809, 28609.572368, 28922.317633, 29235.448741, 29548.944253, 29862.766175, 30176.910610, 30491.363107,
  30806.103787, 31121.126024, 31436.412153, 31751.975134, 32067.737444, 32383.768560, 32700.017044, 33016.458300,
  33333.101934, 33649.904492, 33966.923435, 34284.105041, 34601.429152, 34918.876076, 35236.481998, 35554.235511,
  35872.093847, 36190.101572, 36508.190892, 36826.420800, 37144.739624, 37463.138566, 37781.598984, 38100.191087,
  38418.846511, 38737.587005, 39056.391321, 39375.255819, 39694.182864, 40013.173503, 40332.221146, 40651.311460,
  40970.465534, 41289.697002, 41608.913381, 41928.242461, 42247.585089, 42566.988678, 42886.409594, 43205.849396,
  43525.322840, 43844.784209, 44164.327769, 44483.869861, 44803.383648, 45122.975593, 45442.593765, 45762.258110,
  46081.937012, 46401.605265, 46721.295022, 47041.004034, 47360.695978, 47680.435451, 48000.192231, 48319.953839,
  48639.726508, 48959.506239, 49279.318744, 49599.117846, 49918.951926, 50238.772730, 50558.620076, 50878.455501,
  51198.285377, 51518.135316, 51837.976134, 52157.809260, 52477.635805, 52797.492063, 53117.368983, 53437.262930,
  53757.142921, 54077.026859, 54396.907345, 54716.835955, 55036.713062, 55356.640827, 55676.537369, 55996.488865,
  56316.420754, 56636.355217, 56956.329593, 57276.245282, 57596.202473, 57916.159021, 58236.077854, 58556.010303,
  58875.938110, 59195.924442, 59515.871947, 59835.838035, 60155.809948, 60475.808167, 60795.765545, 61115.766398,
  61435.725825, 61755.677959, 62075.688445, 62395.647263, 62715.609853, 63035.591787, 63355.588060, 63675.579841,
  63995.560980, 64315.552298, 64635.582956, 64955.538779, 65275.512154, 65595.490993, 65915.477332, 66235.470693,
  66555.483426, 66875.455452, 67195.455039, 67515.435090, 67835.418300, 68155.401870, 68475.404599, 68795.452423,
  69115.474466, 69435.450344, 69755.439668, 70075.479966, 70395.468204, 70715.475957, 71035.472807, 71355.513734,
  71675.486047, 71995.450475, 72315.443410, 72635.425138, 72955.481520, 73275.482426, 73595.476688, 73915.469540,
  74235.426693, 74555.381683, 74875.368981, 75195.429157, 75515.480428, 75835.517265, 76155.557945, 76475.556134,
  76795.579451, 77115.605924, 77435.604178, 77755.572770, 78075.576305, 78395.562526, 78715.547599, 79035.551674,
  79355.540615, 79675.575726, 79995.547586, 80315.544278, 80635.546227, 80955.555617, 81275.540591, 81595.549538,
  81915.550079
},
// log K = 14
{
  11817.000969, 12127.609164, 12443.958867, 12766.059919, 13093.926347, 13427.563687, 13766.972021, 14112.158775,
  14463.118632, 14819.833221, 15182.310838, 15550.514164, 15924.452624, 16304.097682, 16689.414687, 17080.390156,
  17476.985675, 17879.171048, 18286.913146, 18700.171223, 19118.909859, 19543.074108, 19972.606221, 20407.466793,
  20847.600290, 21292.965548, 21743.489087, 22199.109276, 22659.760749, 23125.379711, 23595.914325, 24071.277989,
  24551.407611, 25036.233071, 25525.671155, 26019.641791, 26518.074136, 27020.885189, 27528.004081, 28039.347478,
  28554.818908, 29074.343878, 29597.869471, 30125.254970, 30656.449891, 31191.351228, 31729.908970, 32272.003587,
  32817.586623, 33366.531359, 33918.769390, 34474.232727, 35032.798601, 35594.423192, 36159.024745, 36726.469786,
  37296.712851, 37869.686035, 38445.278953, 39023.442285, 39604.084062, 40187.147209, 40772.503600, 41360.148758,
  41949.978377, 42541.929077, 43135.892496, 43731.836459, 44329.664552, 44929.334224, 45530.772542, 46133.919152,
  46738.746702, 47345.120215, 47953.051656, 48562.469011, 49173.281212, 49785.453501, 50398.908717, 51013.645932,
  51629.563526, 52246.635759, 52864.820434, 53484.057447, 54104.303719, 54725.504675, 55347.680019, 55970.744363,
  56594.688890, 57219.458967, 57844.949821, 58471.197998, 59098.180259, 59725.774793, 60354.058215, 60982.962558,
  61612.427469, 62242.448368, 62873.013426, 63504.106743, 64135.672742, 64767.665213, 65400.082326, 66032.949331,
  66666.219558, 67299.817447, 67933.801373, 68568.092593, 69202.717636, 69837.643507, 70472.852133, 71108.305774,
  71744.023189, 72380.016332, 73016.168118, 73652.560876, 74289.210741, 74926.041959, 75563.048434, 76200.207724,
  76837.505542, 77474.999283, 78112.608284, 78750.375633, 79388.254423, 80026.267074, 80664.419197, 81302.602941,
  81940.909776, 82579.321050, 83217.801329, 83856.420605, 84495.098999, 85133.832545, 85772.588001, 86411.448347,
  87050.399262, 87689.358100, 88328.463714, 88967.516990, 89606.618839, 90245.788934, 90884.986443, 91524.243962,
  92163.523370, 92802.835394, 93442.198790, 94081.633840, 94721.043838, 95360.482304, 96000.002974, 96639.518339,
  97279.069377, 97918.584802, 98558.189888, 99197.773242, 99837.390001, 100476.994827, 101116.655652, 101756.293703,
  102395.977437, 103035.662337, 103675.360919, 104315.063845, 104954.783621, 105594.504004, 106234.229823, 106874.056079,
  107513.846129, 108153.562857, 108793.393622, 109433.202056, 110072.966808, 110712.777026, 111352.577741, 111992.441538,
  112632.256702, 113272.083743, 113911.943484, 114551.818432, 115191.687411, 115831.584194, 116471.522453, 117111.338979,
  117751.192777, 118391.070556, 119030.991702, 119670.888488, 120310.801509, 120950.761000, 121590.691826, 122230.618394,
  122870.618097, 123510.616056, 124150.552363, 124790.488946, 125430.445483, 126070.428297, 126710.409643, 127350.398562,
  127990.397846, 128630.413222, 129270.354937, 129910.365912, 130550.332174, 131190.259646, 131830.280970, 132470.304278,
  133110.295205, 133750.312426, 134390.364847, 135030.321000, 135670.319926, 136310.335570, 136950.324790, 137590.338289,
  138230.368657, 138870.374084, 139510.447896, 140150.468353, 140790.441338, 141430.438424, 142070.440787, 142710.431348,
  143350.433770, 143990.493350, 144630.548409, 145270.549935, 145910.530486, 146550.488808, 147190.510290, 147830.509426,
  148470.575641, 149110.541845, 149750.592427, 150390.634921, 151030.706500, 151670.646574, 152310.624482, 152950.686127,
  153590.659153, 154230.646236, 154870.720079, 155510.614028, 156150.596142, 156790.659641, 157430.633386, 158070.649047,
  158710.591350, 159350.585980, 159990.557711, 160630.530183, 161270.499427, 161910.521323, 162550.516603, 163190.482792,
  163830.422631
},
// log K = 15
{
  23634.780143, 24256.008404, 24888.717596, 25532.934303, 26188.680791, 26855.965949, 27534.798395, 28225.179199,
  28927.099457, 29640.545847, 30365.501013, 31101.936533, 31849.825685, 32609.111850, 33379.755958, 34161.706474,
  34954.912131, 35759.291030, 36574.778310, 37401.280667, 38238.742234, 39087.060449, 39946.133936, 40815.861824,
  41696.151280, 42586.877221, 43487.927203, 44399.169293, 45320.460825, 46251.693279, 47192.741847, 48143.464216,
  49103.716679, 50073.349113, 51052.208336, 52040.138165, 53036.993192, 54042.604241, 55056.838449, 56079.501709,
  57110.434199, 58149.484623, 59196.455710, 60251.226284, 61313.593108, 62383.385277, 63460.484960, 64544.666337,
  65635.763495, 66733.629361, 67838.096489, 68948.987037, 70066.117363, 71189.338133, 72318.464573, 73453.423815,
  74593.923438, 75739.864335, 76891.058098, 78047.391508, 79208.654009, 80374.753680, 81545.514022, 82720.817799,
  83900.405263, 85084.273208, 86272.263471, 87464.134340, 88659.829437, 89859.204804, 91062.115479, 92268.425863,
  93478.041907, 94690.804589, 95906.647693, 97125.398400, 98347.018145, 99571.305992, 100798.274503, 102027.737913,
  103259.574749, 104493.727918, 105730.035415, 106968.465700, 108208.988306, 109451.445144, 110695.748927, 111941.827269,
  113189.666448, 114439.093665, 115690.116530, 116942.608958, 118196.501294, 119451.722652, 120708.276299, 121966.046247,
  123225.027480, 124485.082349, 125746.201609, 127008.357433, 128271.416054, 129535.417336, 130800.297278, 132066.008820,
  133332.483576, 134599.733640, 135867.681429, 137136.303792, 138405.538969, 139675.413251, 140945.839375, 142216.787412,
  143488.232199, 144760.234976, 146032.650196, 147305.459198, 148578.703708, 149852.356585, 151126.347770, 152400.641475,
  153675.275168, 154950.179904, 156225.390849, 157500.864126, 158776.585926, 160052.504602, 161328.716398, 162605.171897,
  163881.825931, 165158.677102, 166435.646121, 167712.814846, 168990.136047, 170267.619890, 171545.238277, 172823.011460,
  174100.890250, 175378.821293, 176656.920467, 177935.093547, 179213.318173, 180491.692642, 181770.130424, 183048.727206,
  184327.217835, 185605.921891, 186884.657773, 188163.418059, 189442.221838, 190721.122201, 192000.068271, 193279.087882,
  194558.139554, 195837.195523, 197116.400538, 198395.612565, 199674.831001, 200954.101970, 202233.365695, 203512.639968,
  204792.003319, 206071.379608, 207350.730914, 208630.080321, 209909.544216, 211189.014497, 212468.508049, 213748.055445,
  215027.584964, 216307.216078, 217586.896296, 218866.477232, 220146.109506, 221425.767458, 222705.465633, 223985.129542,
  225264.797531, 226544.544335, 227824.304232, 229104.031191, 230383.739676, 231663.424684, 232943.198829, 234222.906969,
  235502.669185, 236782.475696, 238062.262723, 239342.090234, 240622.002668, 241901.911022, 243181.742902, 244461.690551,
  245741.531359, 247021.432644, 248301.277604, 249581.168404, 250861.094078, 252141.038818, 253421.065594, 254701.020169,
  255980.887518, 257260.848328, 258540.873565, 259820.905666, 261100.908594, 262380.854763, 263660.862699, 264940.834842,
  266220.775656, 267500.745402, 268780.761926, 270060.823540, 271340.798715, 272620.823081, 273900.881190, 275180.928531,
  276460.914606, 277740.919081, 279020.967358, 280301.002010, 281581.054314, 282861.097638, 284141.109728, 285421.181335,
  286701.182750, 287981.231437, 289261.342952, 290541.328315, 291821.320901, 293101.395969, 294381.402286, 295661.374812,
  296941.357112, 298221.462446, 299501.443884, 300781.429735, 302061.512800, 303341.459364, 304621.530042, 305901.507763,
  307181.541613, 308461.506346, 309741.474814, 311021.458944, 312301.373851, 313581.258984, 314861.222655, 316141.192042,
  317421.179698, 318701.162346, 319981.143104, 321261.185706, 322541.120379, 323821.065555, 325100.961639, 326380.920540,
  327660.786948
},
// log K = 16
{
  47270.338530, 48512.804588, 49778.235006, 51066.679846, 52378.178287, 53712.756179, 55070.430016, 56451.198432,
  57855.044557, 59281.941569, 60731.855114, 62204.727445, 63700.498656, 65219.087806, 66760.381754, 68324.278827,
  69910.681844, 71519.442760, 73150.426782, 74803.469853, 76478.400456, 78175.038414, 79893.184924, 81632.639705,
  83393.214587, 85174.662642, 86976.739912, 88799.210643, 90641.829434, 92504.355605, 94386.478165, 96287.925119,
  98208.422967, 100147.694840, 102105.387259, 104081.226364, 106074.916897, 108086.136683, 110114.560800, 112159.857579,
  114221.724675, 116299.785348, 118393.731853, 120503.258946, 122627.958417, 124767.540962, 126921.668848, 129090.003274,
  131272.204811, 133467.918004, 135676.870426, 137898.595565, 140132.829694, 142379.269230, 144637.536478, 146907.321805,
  149188.299797, 151480.151490, 153782.571459, 156095.292246, 158417.834407, 160749.983694, 163091.465145, 165441.984077,
  167801.236994, 170168.903670, 172544.767987, 174928.494171, 177319.918928, 179718.624717, 182124.426670, 184537.056818,
  186956.260737, 189381.869001, 191813.551321, 194251.107949, 196694.280093, 199142.910671, 201596.663557, 204055.453662,
  206519.090402, 208987.322132, 211460.079506, 213936.962995, 216417.945039, 218902.907481, 221391.594168, 223883.857806,
  226379.519239, 228878.478995, 231380.515508, 233885.422831, 236393.251620, 238903.734661, 241416.885791, 243932.462444,
  246450.361381, 248970.497360, 251492.768859, 254017.059221, 256543.244066, 259071.366198, 261601.098326, 264132.472390,
  266665.477130, 269200.003838, 271735.898262, 274273.128446, 276811.699617, 279351.334667, 281892.176977, 284434.126935,
  286977.141855, 289520.993664, 292065.816286, 294611.452586, 297157.986206, 299705.252956, 302253.226506, 304801.859484,
  307351.170990, 309901.148395, 312451.594894, 315002.530644, 317553.961670, 320105.951895, 322658.553440, 325211.299379,
  327764.626147, 330318.311300, 332872.331048, 335426.696106, 337981.358498, 340536.275072, 343091.446562, 345646.972942,
  348202.757347, 350758.693296, 353314.808579, 355871.203754, 358427.702337, 360984.491079, 363541.449032, 366098.493281,
  368655.687887, 371213.030472, 373770.561193, 376328.233445, 378886.001706, 381443.937538, 384001.856504, 386559.857503,
  389117.926075, 391676.219835, 394234.530250, 396792.812601, 399351.291660, 401909.794770, 404468.330377, 407026.964781,
  409585.614496, 412144.407471, 414703.175858, 417261.980659, 419820.958264, 422379.863083, 424938.751186, 427497.927620,
  430056.993719, 432616.066348, 435175.266190, 437734.382772, 440293.531277, 442852.711332, 445412.016423, 447971.502143,
  450530.798765, 453090.167199, 455649.502729, 458208.951251, 460768.459694, 463328.053373, 465887.570627, 468447.239271,
  471006.792818, 473566.544068, 476126.194227, 478685.887605, 481245.577573, 483805.348711, 486365.028302, 488924.844568,
  491484.612666, 494044.321666, 496604.011864, 499163.799789, 501723.629793, 504283.493711, 506843.290195, 509403.157856,
  511962.990320, 514522.941350, 517082.791953, 519642.848656, 522202.833761, 524762.686522, 527322.632758, 529882.529037,
  532442.420851, 535002.422317, 537562.386309, 540122.357425, 542682.434171, 545242.468829, 547802.466694, 550362.492718,
  552922.461624, 555482.539495, 558042.531431, 560602.467437, 563162.648952, 565722.750610, 568282.702877, 570842.810092,
  573402.917604, 575962.999235, 578523.081937, 581083.162584, 583643.265455, 586203.287883, 588763.260931, 591323.292027,
  593883.252456, 596443.273935, 599003.353442, 601563.492606, 604123.421135, 606683.438234, 609243.605174, 611803.638038,
  614363.628593, 616923.690580, 619483.675256, 622043.744171, 624603.673246, 627163.577236, 629723.677960, 632283.670157,
  634843.692958, 637403.576097, 639963.511752, 642523.482942, 645083.419327, 647643.330711, 650203.272467, 652763.290376,
  655323.267522
},
// log K = 17
{
  94541.455324, 97026.403245, 99557.280165, 102134.178452, 104757.187033, 107426.362674, 110141.726029, 112903.278005,
  115710.975458, 118564.785344, 121464.629896, 124410.377345, 127401.910279, 130439.087070, 133521.683723, 136649.499031,
  139822.321627, 143039.848320, 146301.785984, 149607.844773, 152957.695333, 156350.945326, 159787.233040, 163266.157476,
  166787.301371, 170350.201319, 173954.353438, 177599.302692, 181284.526367, 185009.507089, 188773.757457, 192576.638207,
  196417.619925, 200296.089540, 204211.494530, 208163.221220, 212150.613086, 216173.056150, 220229.879308, 224320.462264,
  228444.146459, 232600.284426, 236788.187347, 241007.264352, 245256.725247, 249535.938618, 253844.217048, 258180.876528,
  262545.282090, 266936.686787, 271354.453768, 275797.958112, 280266.429404, 284759.298770, 289275.861948, 293815.386243,
  298377.390708, 302961.087179, 307565.895452, 312191.173759, 316836.362522, 321500.721532, 326183.652758, 330884.723656,
  335603.197219, 340338.617624, 345090.316855, 349857.860719, 354640.538362, 359438.001710, 364249.638745, 369074.940533,
  373913.351331, 378764.438864, 383627.767868, 388502.854215, 393389.259584, 398286.483436, 403194.238263, 408111.948151,
  413039.292303, 417975.909674, 422921.304084, 427875.195485, 432837.200959, 437807.062429, 442784.399966, 447768.726662,
  452760.032525, 457757.794185, 462761.810279, 467771.737196, 472787.226777, 477808.283249, 482834.411114, 487865.521166,
  492901.275392, 497941.616150, 502986.164281, 508034.749030, 513087.210697, 518143.298172, 523202.692981, 528265.454984,
  533331.384435, 538400.437943, 543472.278711, 548546.790172, 553623.737338, 558703.047575, 563784.666463, 568868.524932,
  573954.251207, 579041.935016, 584131.557779, 589222.910016, 594315.786547, 599410.314112, 604506.227555, 609603.610432,
  614702.124262, 619801.918486, 624902.903258, 630005.085347, 635107.990499, 640211.847431, 645316.755403, 650422.424613,
  655529.009211, 660636.166872, 665744.170495, 670852.806947, 675962.099161, 681072.042796, 686182.458370, 691293.269596,
  696404.763335, 701516.635253, 706628.965299, 711741.575313, 716854.769083, 721968.220605, 727082.027784, 732196.114131,
  737310.594653, 742425.339665, 747540.295793, 752655.505647, 757770.968129, 762886.636891, 768002.527720, 773118.559142,
  778234.871441, 783351.273881, 788467.944809, 793584.599211, 798701.497594, 803818.484285, 808935.619316, 814053.067243,
  819170.390229, 824287.946609, 829405.450988, 834523.054071, 839640.856519, 844758.800102, 849876.719924, 854994.831607,
  860112.896788, 865231.116455, 870349.453898, 875467.910756, 880586.444976, 885705.102070, 890823.822978, 895942.513436,
  901061.120048, 906179.716020, 911298.587548, 916417.583647, 921536.507373, 926655.570709, 931774.690027, 936893.879961,
  942012.956398, 947132.142141, 952251.503479, 957370.815448, 962490.012685, 967609.521437, 972729.002837, 977848.339983,
  982967.824448, 988087.392216, 993206.992691, 998326.635354, 1003446.304388, 1008565.985024, 1013685.706678, 1018805.581548,
  1023925.239073, 1029045.157502, 1034165.035124, 1039284.843524, 1044404.676526, 1049524.620186, 1054644.441170, 1059764.409794,
  1064884.318434, 1070004.338968, 1075124.268749, 1080244.471055, 1085364.528193, 1090484.511927, 1095604.595114, 1100724.598478,
  1105844.666500, 1110964.804168, 1116084.864159, 1121204.874577, 1126325.062599, 1131445.152321, 1136565.301592, 1141685.638897,
  1146805.806800, 1151925.790859, 1157045.932640, 1162166.112443, 1167286.221698, 1172406.273611, 1177526.581875, 1182646.832239,
  1187766.882661, 1192886.884388, 1198006.962839, 1203127.084377, 1208246.959060, 1213366.976076, 1218486.763464, 1223606.758568,
  1228726.721761, 1233846.593404, 1238966.815228, 1244086.865449, 1249206.854850, 1254326.996667, 1259447.092239, 1264567.198081,
  1269687.499091, 1274807.474194, 1279927.244161, 1285047.273317, 1290167.090035, 1295287.035620, 1300406.888764, 1305526.667946,
  1310646.540340
},
// log K = 18
{
  189083.688921, 194053.597973, 199115.342781, 204269.157017, 209515.195566, 214853.553887, 220284.295855, 225807.399998,
  231422.826900, 237130.469824, 242930.139690, 248821.634191, 254804.718978, 260879.073467, 267044.289594, 273299.936993,
  279645.549742, 286080.586199, 292604.521050, 299216.651567, 305916.376160, 312702.908374, 319575.536730, 326533.420485,
  333575.639430, 340701.388339, 347909.713977, 355199.642852, 362570.108280, 370020.154080, 377548.652175, 385154.413997,
  392836.374125, 400593.371525, 408424.172521, 416327.671123, 424302.406749, 432347.292674, 440461.014310, 448642.241683,
  456889.603709, 465201.946081, 473577.749277, 482015.802141, 490514.770444, 499073.243760, 507689.794308, 516363.149230,
  525091.902823, 533874.850510, 542710.434311, 551597.433198, 560534.241273, 569520.019389, 578553.034265, 587632.180111,
  596756.084542, 605923.440522, 615133.037840, 624383.626242, 633673.841133, 643002.674316, 652368.578283, 661770.556501,
  671207.605795, 680678.417768, 690181.818697, 699716.780471, 709282.084973, 718876.864175, 728499.951143, 738150.280049,
  747827.053968, 757529.236597, 767255.784062, 777006.100829, 786779.065927, 796573.507429, 806388.828153, 816223.976258,
  826078.608350, 835951.751956, 845842.493689, 855750.225870, 865674.190527, 875613.809349, 885568.425527, 895537.272219,
  905519.763307, 915515.310346, 925523.353103, 935543.172648, 945574.292664, 955616.280042, 965668.428231, 975730.535479,
  985802.055447, 995882.596628, 1005971.583108, 1016068.664992, 1026173.649961, 1036285.774891, 1046404.955770, 1056530.588186,
  1066662.648243, 1076800.535542, 1086944.269881, 1097093.058652, 1107247.076183, 1117405.990557, 1127569.310917, 1137737.011345,
  1147908.717700, 1158084.362020, 1168263.501029, 1178446.221907, 1188632.206842, 1198821.131431, 1209013.020373, 1219207.570786,
  1229404.854893, 1239604.423801, 1249806.433263, 1260010.619993, 1270216.819018, 1280424.774173, 1290634.560600, 1300846.097203,
  1311059.128630, 1321273.628402, 1331489.832488, 1341707.300774, 1351925.947953, 1362145.802925, 1372366.802414, 1382588.547896,
  1392811.264776, 1403035.227449, 1413259.922280, 1423485.322819, 1433711.916106, 1443938.981360, 1454166.596984, 1464394.761679,
  1474623.684212, 1484853.156422, 1495083.020146, 1505313.735890, 1515544.731764, 1525776.086634, 1536007.742073, 1546239.679012,
  1556472.212370, 1566704.988763, 1576937.965495, 1587171.446007, 1597405.292186, 1607639.395274, 1617873.660775, 1628108.037273,
  1638342.741799, 1648577.832828, 1658813.325573, 1669048.803784, 1679284.679963, 1689520.927615, 1699757.050010, 1709993.263665,
  1720229.557663, 1730466.102090, 1740702.604009, 1750939.618504, 1761176.930182, 1771414.210528, 1781651.713742, 1791889.218503,
  1802126.805234, 1812364.257333, 1822602.054007, 1832839.687792, 1843077.871973, 1853315.944762, 1863554.202066, 1873792.633125,
  1884030.883830, 1894269.182711, 1904507.712050, 1914746.469507, 1924985.484753, 1935224.245956, 1945463.225215, 1955702.268883,
  1965941.321722, 1976180.037370, 1986419.052784, 1996658.429579, 2006897.450283, 2017136.904971, 2027376.240039, 2037615.549295,
  2047855.197425, 2058094.765906, 2068334.279787, 2078573.820075, 2088813.469730, 2099053.348620, 2109293.174176, 2119533.012704,
  2129772.820132, 2140012.744709, 2150252.607739, 2160492.533017, 2170732.406422, 2180972.400110, 2191212.436319, 2201452.637894,
  2211692.339292, 2221932.460057, 2232172.746036, 2242412.892705, 2252653.174824, 2262893.432271, 2273134.002270, 2283374.311008,
  2293614.537881, 2303854.703732, 2314095.191374, 2324335.236186, 2334575.624526, 2344816.313269, 2355056.224171, 2365296.361285,
  2375537.048184, 2385777.280284, 2396017.222502, 2406257.145546, 2416497.272190, 2426737.212210, 2436977.500856, 2447217.897426,
  2457458.423605, 2467698.536697, 2477938.448096, 2488178.544726, 2498418.640441, 2508658.160374, 2518898.274852, 2529138.509345,
  2539378.310538, 2549617.989497, 2559857.504886, 2570097.363128, 2580337.195261, 2590576.878833, 2600816.572159, 2611055.930087,
  2621295.625004
},
// log K = 19
{
  378168.156126, 388107.986863, 398231.517433, 408539.178530, 419031.252008, 429707.954086, 440569.365328, 451615.642722,
  462846.490174, 474261.790112, 485861.190310, 497644.259253, 509610.438730, 521759.095095, 534089.573442, 546600.981190,
  559292.272697, 572162.409622, 585210.331052, 598434.669889, 611834.157416, 625407.271721, 639152.543961, 653068.262294,
  667152.777393, 681404.241581, 695820.778241, 710400.501586, 725141.425404, 740041.558661, 755098.503731, 770310.107475,
  785674.192935, 801188.297422, 816849.950298, 832656.623960, 848606.198026, 864696.151343, 880923.487841, 897285.841319,
  913780.530043, 930405.131973, 947156.655545, 964032.974599, 981030.762278, 998147.499138, 1015380.659035, 1032727.149847,
  1050184.616751, 1067750.330789, 1085421.716664, 1103195.771853, 1121069.796650, 1139041.324454, 1157107.373802, 1175265.377022,
  1193513.201704, 1211847.872855, 1230267.133114, 1248768.293478, 1267348.634472, 1286005.987451, 1304738.187318, 1323542.421988,
  1342416.458954, 1361357.807871, 1380364.530293, 1399434.095493, 1418564.587724, 1437754.116682, 1457000.254889, 1476301.275902,
  1495654.977143, 1515059.332212, 1534512.821906, 1554013.130304, 1573558.585534, 1593147.244450, 1612777.978405, 1632448.600136,
  1652157.704100, 1671904.308928, 1691686.012962, 1711501.716352, 1731349.849417, 1751229.053668, 1771138.423208, 1791076.196899,
  1811041.338260, 1831032.177526, 1851048.091817, 1871088.096683, 1891150.317142, 1911234.619162, 1931339.423184, 1951463.947205,
  1971606.994543, 1991767.606441, 2011945.852451, 2032140.098239, 2052349.709954, 2072574.274980, 2092812.387905, 2113063.537955,
  2133327.750182, 2153603.787963, 2173890.933053, 2194188.225246, 2214496.333997, 2234814.120065, 2255140.753372, 2275476.675949,
  2295820.689602, 2316172.220323, 2336530.258616, 2356894.932256, 2377266.633368, 2397645.173978, 2418028.419639, 2438417.586475,
  2458812.422593, 2479211.306360, 2499615.253217, 2520023.375080, 2540436.051898, 2560851.967345, 2581271.569076, 2601694.318944,
  2622120.693963, 2642549.418269, 2662981.070023, 2683415.520909, 2703852.500003, 2724291.876933, 2744733.213126, 2765177.477758,
  2785623.320019, 2806070.985142, 2826520.234343, 2846971.203929, 2867423.303616, 2887876.396540, 2908331.739769, 2928788.290672,
  2949245.276635, 2969704.620226, 2990164.657583, 3010625.841710, 3031087.855626, 3051550.619090, 3072014.642350, 3092479.163042,
  3112944.278087, 3133410.101603, 3153876.719100, 3174343.414117, 3194810.517970, 3215278.762802, 3235747.174277, 3256216.390486,
  3276685.652553, 3297155.394593, 3317625.911419, 3338096.547090, 3358567.567862, 3379038.637659, 3399510.649493, 3419983.382105,
  3440456.231853, 3460929.496047, 3481403.703904, 3501877.874941, 3522351.898403, 3542825.527074, 3563300.038829, 3583775.102749,
  3604249.896903, 3624724.967423, 3645201.027293, 3665676.534460, 3686152.061202, 3706628.308333, 3727104.271827, 3747580.803335,
  3768057.710876, 3788534.660048, 3809011.720864, 3829489.164523, 3849967.204462, 3870445.043912, 3890923.080446, 3911400.767281,
  3931879.061622, 3952357.218696, 3972836.284463, 3993314.516935, 4013793.278282, 4034272.661280, 4054751.814018, 4075230.503334,
  4095708.557968, 4116187.919814, 4136667.714093, 4157147.152355, 4177627.302553, 4198107.383728, 4218587.174918, 4239066.631662,
  4259545.994167, 4280026.100110, 4300506.380609, 4320986.617208, 4341466.696312, 4361945.995732, 4382426.527708, 4402907.058309,
  4423386.556967, 4443867.498542, 4464348.284664, 4484828.344391, 4505309.026083, 4525789.774619, 4546270.396129, 4566750.818685,
  4587231.362126, 4607711.356124, 4628191.883250, 4648673.308942, 4669153.953372, 4689634.118530, 4710114.637510, 4730595.217429,
  4751075.358693, 4771555.492921, 4792035.313408, 4812516.057037, 4832995.761283, 4853475.977619, 4873956.732160, 4894436.879314,
  4914917.149285, 4935397.069776, 4955877.550351, 4976357.852728, 4996838.246842, 5017318.023169, 5037798.008344, 5058278.290403,
  5078757.968956, 5099237.419344, 5119716.759591, 5140195.935830, 5160675.636320, 5181154.980843, 5201633.780713, 5222113.031789,
  5242591.881577
},
// log K = 20
{
  756337.090537, 776216.744995, 796463.785646, 817079.035290, 838063.221300, 859416.678362, 881139.576270, 903232.151726,
  925693.940877, 948524.600346, 971723.442348, 995289.632784, 1019222.059448, 1043519.402588, 1068180.163485, 1093202.854610,
  1118585.515820, 1144326.031845, 1170421.828997, 1196870.617641, 1223669.453959, 1250815.679160, 1278306.298944, 1306137.726017,
  1334306.782451, 1362809.672011, 1391643.048887, 1420802.665486, 1450284.419390, 1480084.556504, 1510198.362531, 1540621.709038,
  1571349.988582, 1602377.885766, 1633700.853485, 1665314.443974, 1697213.607484, 1729393.242718, 1761847.799154, 1794572.464804,
  1827562.002973, 1860811.213417, 1894314.858503, 1928067.079352, 1962062.774535, 1996296.400592, 2030762.354026, 2065455.981656,
  2100370.818573, 2135502.224529, 2170844.722018, 2206392.452100, 2242140.795895, 2278083.565225, 2314215.470175, 2350532.238358,
  2387028.028531, 2423697.739702, 2460535.617283, 2497537.908190, 2534699.627071, 2572014.508248, 2609478.240813, 2647086.878671,
  2684834.738503, 2722717.495987, 2760730.659130, 2798869.445379, 2837130.937688, 2875509.782410, 2914002.086936, 2952603.395700,
  2991310.971904, 3030119.629799, 3069026.891217, 3108027.543585, 3147118.485322, 3186296.724369, 3225557.893026, 3264899.405158,
  3304317.806643, 3343809.532357, 3383372.875494, 3423003.239113, 3462699.855290, 3502458.588120, 3542276.984489, 3582151.461666,
  3622080.455509, 3662062.087297, 3702093.774268, 3742173.351913, 3782298.542025, 3822466.599295, 3862676.059061, 3902925.301466,
  3943212.313188, 3983534.655139, 4023890.682932, 4064278.948819, 4104698.644146, 4145147.867936, 4185624.200116, 4226127.607823,
  4266655.471909, 4307207.261933, 4347781.577688, 4388376.075665, 4428991.084860, 4469625.512791, 4510278.322018, 4550949.135583,
  4591635.061142, 4632337.290243, 4673054.034167, 4713783.999697, 4754527.016825, 4795282.199016, 4836049.304645, 4876828.217063,
  4917617.432795, 4958416.033283, 4999223.332994, 5040040.200620, 5080865.836319, 5121698.006953, 5162537.663489, 5203383.861562,
  5244235.368756, 5285093.542054, 5325957.172545, 5366826.006832, 5407700.602295, 5448579.444589, 5489462.237514, 5530348.767163,
  5571240.286944, 5612135.490023, 5653033.590430, 5693935.090249, 5734840.012969, 5775747.413811, 5816658.159197, 5857571.727542,
  5898486.810748, 5939403.918361, 5980324.159335, 6021245.922584, 6062167.462275, 6103093.061724, 6144019.021028, 6184948.477708,
  6225878.111073, 6266809.926593, 6307741.380274, 6348674.587241, 6389609.653586, 6430546.024311, 6471482.661256, 6512419.658468,
  6553358.313587, 6594299.462793, 6635239.780670, 6676180.809115, 6717122.614963, 6758064.640997, 6799009.935719, 6839954.567726,
  6880900.950276, 6921847.965357, 6962794.580261, 7003742.234176, 7044691.155209, 7085639.223984, 7126587.984374, 7167538.597843,
  7208487.508674, 7249437.307369, 7290389.448350, 7331341.752887, 7372292.872774, 7413245.082344, 7454198.512431, 7495151.878502,
  7536105.815461, 7577059.755263, 7618013.175400, 7658967.579066, 7699922.475951, 7740878.015144, 7781833.511721, 7822789.986990,
  7863745.987999, 7904702.500036, 7945659.757785, 7986615.385020, 8027573.168319, 8068531.917672, 8109489.438412, 8150447.742963,
  8191403.350221, 8232362.807587, 8273321.255913, 8314281.043410, 8355240.292724, 8396199.214301, 8437156.471990, 8478114.862372,
  8519073.457296, 8560034.832965, 8600993.512814, 8641954.368755, 8682914.667061, 8723875.362809, 8764837.809961, 8805797.690078,
  8846758.789178, 8887720.671501, 8928680.126482, 8969640.467726, 9010601.160006, 9051561.769905, 9092522.487783, 9133484.594542,
  9174446.122191, 9215406.809237, 9256366.837569, 9297328.747584, 9338288.901510, 9379250.948160, 9420212.503729, 9461173.228802,
  9502133.928845, 9543094.489131, 9584055.513956, 9625015.618922, 9665975.737758, 9706937.403885, 9747896.035874, 9788856.165941,
  9829816.994627, 9870777.228642, 9911737.327683, 9952698.937964, 9993660.635143, 10034620.747904, 10075579.526207, 10116539.739394,
  10157498.625700, 10198458.468474, 10239418.486051, 10280376.431741, 10321335.494132, 10362295.312860, 10403254.402980, 10444214.519042,
  10485173.027410
},
// log K = 21
{
  1512674.959317, 1552434.197368, 1592928.155075, 1634158.593696, 1676126.959176, 1718834.017325, 1762279.726817, 1806464.610827,
  1851388.162884, 1897049.337397, 1943446.849678, 1990579.312415, 2038444.063365, 2087038.766553, 2136360.248426, 2186405.470599,
  2237170.640174, 2288651.015887, 2340842.752937, 2393739.986364, 2447337.958039, 2501630.515180, 2556611.361814, 2612274.289376,
  2668612.210872, 2725618.064986, 2783284.549430, 2841603.566294, 2900566.895724, 2960167.093438, 3020394.610851, 3081240.447614,
  3142696.078921, 3204751.105703, 3267397.808234, 3330624.834407, 3394422.872136, 3458781.966184, 3523690.805899, 3589140.856689,
  3655119.540256, 3721617.907853, 3788624.486645, 3856129.175227, 3924119.940026, 3992586.658818, 4061519.544440, 4130906.734075,
  4200737.500257, 4271000.909057, 4341685.842431, 4412781.306685, 4484277.199691, 4556162.287552, 4628426.495554, 4701059.642462,
  4774050.909933, 4847389.117100, 4921065.536469, 4995068.178578, 5069389.529141, 5144019.928509, 5218947.440841, 5294164.568050,
  5369660.364896, 5445425.915267, 5521454.727645, 5597734.642433, 5674257.411718, 5751014.463556, 5827999.822090, 5905203.759793,
  5982617.522812, 6060234.561845, 6138048.162353, 6216049.451496, 6294232.713331, 6372588.108087, 6451109.903764, 6529792.611180,
  6608629.912527, 6687615.097432, 6766740.086064, 6846000.116450, 6925391.839995, 7004908.093083, 7084544.127544, 7164293.822313,
  7244153.392582, 7324115.814384, 7404179.031163, 7484336.380737, 7564586.128001, 7644922.247694, 7725340.819662, 7805840.541693,
  7886412.416887, 7967054.301986, 8047764.087248, 8128539.447460, 8209376.477465, 8290273.766928, 8371225.884580, 8452230.183873,
  8533283.959811, 8614388.863382, 8695539.350564, 8776730.375553, 8857961.046732, 8939230.757845, 9020535.369667, 9101877.322129,
  9183251.420601, 9264654.743697, 9346087.109813, 9427548.372707, 9509034.441574, 9590547.753266, 9672081.682514, 9753639.600816,
  9835216.139507, 9916813.989591, 9998428.682824, 10080058.312759, 10161706.673718, 10243372.018016, 10325050.507034, 10406744.529470,
  10488447.296300, 10570163.109725, 10651893.512546, 10733632.712879, 10815382.384056, 10897140.573621, 10978907.646650, 11060681.383125,
  11142464.138730, 11224254.549571, 11306053.275368, 11387858.162207, 11469666.329635, 11551480.634292, 11633302.025569, 11715128.710512,
  11796961.403328, 11878795.670820, 11960634.652330, 12042477.348124, 12124323.950451, 12206172.128053, 12288028.811447, 12369886.306570,
  12451744.123236, 12533607.183832, 12615473.707341, 12697338.733240, 12779207.987968, 12861080.507718, 12942957.260823, 13024834.007606,
  13106715.252745, 13188597.806270, 13270478.933580, 13352362.482281, 13434247.263704, 13516133.477076, 13598020.834213, 13679909.264273,
  13761799.592878, 13843689.299819, 13925583.582108, 14007479.173806, 14089371.780210, 14171268.621526, 14253167.561983, 14335070.527750,
  14416971.620797, 14498873.784867, 14580778.789301, 14662681.662290, 14744586.311912, 14826493.286700, 14908400.702409, 14990305.605573,
  15072214.379125, 15154123.120545, 15236031.901296, 15317939.866920, 15399849.993076, 15481761.939120, 15563672.325616, 15645585.312945,
  15727497.406318, 15809411.780271, 15891325.875461, 15973239.145687, 16055155.936424, 16137069.783844, 16218984.663574, 16300899.732679,
  16382815.849682, 16464730.053474, 16546645.675799, 16628563.444017, 16710481.533611, 16792400.824636, 16874319.061886, 16956235.859045,
  17038151.394583, 17120072.629220, 17201992.200096, 17283914.365655, 17365836.161356, 17447756.880495, 17529681.545942, 17611601.675003,
  17693522.079185, 17775441.939609, 17857361.777214, 17939284.144858, 18021205.445833, 18103125.675947, 18185051.132189, 18266974.391463,
  18348894.689783, 18430817.526979, 18512736.992850, 18594657.001222, 18676577.636496, 18758497.698999, 18840421.426602, 18922345.360722,
  19004266.906157, 19086186.184618, 19168105.320223, 19250029.336282, 19331950.350200, 19413874.580826, 19495794.431194, 19577715.745558,
  19659638.264924, 19741557.363469, 19823478.431258, 19905400.862401, 19987318.682409, 20069238.585823, 20151157.549449, 20233076.181910,
  20314994.521260, 20396915.069140, 20478836.108717, 20560753.915833, 20642672.570035, 20724588.867440, 20806507.038063, 20888426.370670,
  20970344.006053
}
};
 
template<typename A>
const double* CompositeInterpolationXTable<A>::get_x_arr(uint8_t logK) {
  if (logK < hll_constants::MIN_LOG_K || logK > hll_constants::MAX_LOG_K) {
    throw std::invalid_argument("logK must be in range [" + std::to_string(hll_constants::MIN_LOG_K)
                                + ", " + std::to_string(hll_constants::MAX_LOG_K) + "]. Found: "
                                + std::to_string(logK));
  }
  return xArray[logK - hll_constants::MIN_LOG_K];
}
 
}
 
#endif // _COMPOSITEINTERPOLATIONXTABLE_INTERNAL_HPP_