package com.yahoo.sketches.hll;

import org.testng.Assert;
import org.testng.annotations.DataProvider;
import org.testng.annotations.Test;

public class HipHllSketchTest
{
  @Test(dataProvider = "sketches")
  public void testEstimation(HllSketch sketch)
  {
    int numEntries = sketch.numBuckets();
    for (int i = 0; i < numEntries * 3; ++i) {
      sketch.update(new int[]{i});

      double estimate = sketch.getEstimate();
      Assert.assertEquals(estimate, estimatesAtLog10Buckets[i], 0.0000001);
      Assert.assertTrue(estimate < sketch.getUpperBound(4.0) + 0.0001);
      Assert.assertTrue(sketch.getLowerBound(4.0) - 0.0001 < estimate);
      Assert.assertEquals(sketch.inversePowerOf2Sum(), inversePow2Vals[i], 0.0000001);
    }
  }

  @Test(dataProvider = "sketches")
  public void testEstimationSanity(HllSketch sketch)
  {
    int numberOfUniques = 1000000;
    for (int i = 0; i < numberOfUniques; i++) {
      sketch.update(new int[]{i});
    }
    Assert.assertEquals(sketch.getEstimate(), numberOfUniques, numberOfUniques * 0.01);
  }

  @Test
  public void testNoUnion()
  {
    HllSketchBuilder bob = HllSketch.builder().setLogBuckets(10).setHipEstimator(true);

    HllSketch sketch = bob.build();
    sketch.update(new long[]{182748912741928L});

    boolean exceptionCaught = false;
    HllSketch unionInto = bob.build();
    try {
      unionInto.union(sketch);
    }
    catch (UnsupportedOperationException e) {
      exceptionCaught = true;
    }

    Assert.assertTrue(exceptionCaught, "Expected exception to be thrown");
  }

  @Test
  public void testNoUnionByte()
  {
    HllSketchBuilder bob = HllSketch.builder().setLogBuckets(10).setHipEstimator(true);

    HllSketch sketch = bob.build();
    sketch.update(new byte[]{18, 27, 48, 91, 27, 41, 92, 8});

    boolean exceptionCaught = false;
    HllSketch unionInto = bob.build();
    try {
      unionInto.union(sketch);
    }
    catch (UnsupportedOperationException e) {
      exceptionCaught = true;
    }

    Assert.assertTrue(exceptionCaught, "Expected exception to be thrown");
  }

  @DataProvider(name = "sketches")
  public static Object[][] getSketches()
  {
    HllSketchBuilder bob = HllSketch.builder().setLogBuckets(10).setHipEstimator(true);
    return new Object[][]{
        {bob.build()},
        {bob.copy().setDenseMode(true).build()},
        {bob.copy().setCompressedDense(true).build()}
    };
  }

  public static void main(String[] args)
  {
    HllSketch sketch = (HllSketch) getSketches()[0][0];

    int numEntries = sketch.numBuckets();
    for (int i = 0; i < numEntries * 3; ++i) {
      if (i % 4 == 0) {
        System.out.println();
      }

      sketch.update(new int[]{i});
      System.out.printf("%.20fd, ", sketch.getEstimate());
    }
  }

  private static final double[] estimatesAtLog10Buckets = new double[]{
      1.00000000000000000000d, 2.00085522296884570000d, 3.00219980187118000000d, 4.00403421547030000000d,
      5.00660428033384200000d, 6.00966537988079900000d, 7.01346393397956100000d, 8.01812422340806200000d,
      9.02364772899294000000d, 10.02966516728349500000d, 11.03617702377692200000d, 12.04318378468657300000d,
      13.05068593694336700000d, 14.05868396819721200000d, 15.06742673386646400000d, 16.07666660081238000000d,
      17.08665303898276700000d, 18.09738715372675300000d, 19.10899495812290000000d, 20.12110269224694300000d,
      21.13396124813220600000d, 22.14732097104166000000d, 23.16118235718027300000d, 24.17554590349032800000d,
      25.19066362344076300000d, 26.20653663931378000000d, 27.22291381052966000000d, 28.24017445873530000000d,
      29.25819359630209600000d, 30.27697235516293300000d, 31.29651186978645300000d, 32.31681327718463600000d,
      33.33762324603199000000d, 34.35894228355848400000d, 35.38077089775332000000d, 36.40310959736645000000d,
      37.42595889191009000000d, 38.44893591488711600000d, 39.47267997887112000000d, 40.49693604288712000000d,
      41.52170461931944000000d, 41.52170461931944000000d, 42.54724292678063000000d, 43.57355212247093600000d,
      44.60082655973973000000d, 45.62861653527452000000d, 46.65730994897452000000d, 47.68652032651080000000d,
      48.71650712477572000000d, 49.74701218798724000000d, 50.77829562727722400000d, 51.81009863754235000000d,
      52.84242174257669000000d, 53.87526546696678000000d, 54.90889110572774000000d, 55.94303867878840000000d,
      56.97770871352159000000d, 58.01290173809984000000d, 59.04861828149702000000d, 60.08485887348993500000d,
      61.12188653346841000000d, 62.15970245796325000000d, 63.19853833280077000000d, 64.23790141840993000000d,
      65.27818841164782000000d, 66.31900408995040000000d, 67.36061380418163000000d, 68.40315142627446000000d,
      69.44622002407806000000d, 70.49021913198898000000d, 71.53501714238340000000d, 72.58061527889062000000d,
      73.62674751398943000000d, 74.67368192083948000000d, 75.72115179265485000000d, 76.76942588971490000000d,
      77.81850544790282000000d, 78.86812266818534000000d, 79.91827810195772000000d, 80.96937673868587000000d,
      82.02101510962203000000d, 83.07359935041094000000d, 84.12672485258031000000d, 85.18086672164900000000d,
      86.23595897138335000000d, 87.29200331699552000000d, 87.29200331699552000000d, 88.34912082647209000000d,
      89.40705744971454000000d, 90.46595131150382000000d, 91.52587271015497000000d, 92.58634294430115000000d,
      93.64708780939350000000d, 94.70865742144501000000d, 95.77077757767728000000d, 96.83393154487550000000d,
      97.89763770124368000000d, 98.96217321770649000000d, 100.02726235976496000000d, 101.09318302076068000000d,
      102.15965874938999000000d, 103.22669012404604000000d, 104.29427772402650000000d, 105.36270075015996000000d,
      106.43168145383164000000d, 107.50122041751993000000d, 107.50122041751993000000d, 108.57159786537790000000d,
      109.64295520790950000000d, 110.71515388925694000000d, 111.78791419764934000000d, 112.86165877043545000000d,
      113.93638941541160000000d, 115.01210794535923000000d, 116.08881617806333000000d, 117.16662227953525000000d,
      117.16662227953525000000d, 117.16662227953525000000d, 118.24497815540322000000d, 119.32432859514103000000d,
      120.40424818120701000000d, 121.48473751414465000000d, 122.56579719544847000000d, 123.64742782756598000000d,
      124.72991601758282000000d, 125.81297666871487000000d, 126.89661038676110000000d, 127.98081777848263000000d,
      129.06559945160475000000d, 130.15095601481895000000d, 131.23688807778498000000d, 132.32339625113290000000d,
      133.41048114646514000000d, 134.49843227366060000000d, 135.58696165611417000000d, 136.67657692562503000000d,
      137.76731655680803000000d, 138.85863741206680000000d, 139.95054011116710000000d, 141.04302527486650000000d,
      142.13609352491653000000d, 143.22974548406478000000d, 144.32427417669620000000d, 145.41902227237975000000d,
      146.51435587312852000000d, 147.61071561616922000000d, 148.70795644124289000000d, 149.80578544151092000000d,
      150.90471897159340000000d, 152.00468540328188000000d, 153.10568668007780000000d, 154.20757651799562000000d,
      155.31005952721438000000d, 156.41358212437206000000d, 157.51769965250736000000d, 157.51769965250736000000d,
      157.51769965250736000000d, 158.62271078085430000000d, 159.72861695702710000000d, 160.83512063771866000000d,
      161.94274638136386000000d, 163.05127141519336000000d, 164.16069720067550000000d, 165.27072430094648000000d,
      166.38135336819160000000d, 167.49258505565770000000d, 168.60438229380787000000d, 169.71678342087444000000d,
      170.82978909323612000000d, 171.94370281659334000000d, 173.05852607383147000000d, 174.17395651261012000000d,
      175.28969079024980000000d, 176.40633757845904000000d, 177.52405085062196000000d, 178.64237445732480000000d,
      179.76130906548596000000d, 180.88116142869978000000d, 182.00208641074062000000d, 183.12416290973044000000d,
      183.12416290973044000000d, 184.24731629447766000000d, 185.37108597107837000000d, 186.49605163985070000000d,
      187.62163559148576000000d, 188.74814824275090000000d, 189.87528087896442000000d, 191.00303418292918000000d,
      192.13109807717320000000d, 193.26009476956568000000d, 194.39002580404843000000d, 195.52104886079290000000d,
      196.65324428612632000000d, 196.65324428612632000000d, 197.78653611707327000000d, 198.92045541944714000000d,
      200.05555310546626000000d, 201.19189073312566000000d, 202.32945126844010000000d, 203.46796038019590000000d,
      204.60765743947977000000d, 205.74854492794660000000d, 205.74854492794660000000d, 206.89006832938534000000d,
      206.89006832938534000000d, 208.03222835308740000000d, 208.03222835308740000000d, 209.17502570953150000000d,
      210.31894011144453000000d, 211.46405377362063000000d, 212.60948766333487000000d, 213.75556254573000000000d,
      213.75556254573000000000d, 214.90284122507106000000d, 216.05124573205407000000d, 217.20029456172006000000d,
      218.34998843748100000000d, 219.50032808396780000000d, 219.50032808396780000000d, 220.65163774789977000000d,
      221.80359499948614000000d, 222.95676844355717000000d, 224.11022603547508000000d, 225.26433363431280000000d,
      226.41909197307905000000d, 227.57450178602312000000d, 228.73113509641297000000d, 229.88842199888344000000d,
      231.04636323251773000000d, 232.20495953765342000000d, 233.36453984092500000000d, 234.52539361826980000000d,
      235.68690576757060000000d, 236.84965437924848000000d, 238.01255773384563000000d, 239.17612178792606000000d,
      240.34034729266480000000d, 240.34034729266480000000d, 241.50523500051858000000d, 242.67111742671250000000d,
      243.83816250689165000000d, 245.00554019995980000000d, 246.17416688172410000000d, 247.34404522765720000000d,
      248.51459222475478000000d, 249.68580863779730000000d, 249.68580863779730000000d, 250.85769523287810000000d,
      252.03075649389746000000d, 253.20507894159715000000d, 254.38007513168060000000d, 255.55574583768220000000d,
      256.73268335059000000000d, 257.91063627632985000000d, 259.08926711791355000000d, 260.26891629756270000000d,
      261.44975576458495000000d, 262.63127647491080000000d, 263.81407663734370000000d, 264.99756030792000000000d,
      266.18207072317466000000d, 267.36778126115536000000d, 268.55417867604870000000d, 269.74186613244103000000d,
      270.93058764373677000000d, 272.11999952587730000000d, 273.30975689423620000000d, 274.50055192653355000000d,
      275.69255985676210000000d, 276.88587006534010000000d, 278.08039830360417000000d, 279.27562367588104000000d,
      279.27562367588104000000d, 280.47154699634930000000d, 281.66816908061460000000d, 282.86549074571310000000d,
      284.06351281011484000000d, 285.26276254706530000000d, 286.46271494153206000000d, 287.66337081739200000000d,
      288.86508346328320000000d, 288.86508346328320000000d, 290.06750165661026000000d, 291.27115655352930000000d,
      291.27115655352930000000d, 292.47587350864836000000d, 293.68183190293655000000d, 294.88796785457040000000d,
      294.88796785457040000000d, 296.09481455874230000000d, 297.30237285361164000000d, 298.51064357882115000000d,
      299.72016308199090000000d, 300.93075502258444000000d, 302.14242130407274000000d, 303.35534339581550000000d,
      304.56898426286057000000d, 305.78298483711010000000d, 306.99833621452444000000d, 308.21440925016090000000d,
      309.43188294023787000000d, 310.65008081188620000000d, 311.86970693662914000000d, 313.08960548937705000000d,
      314.31091352787837000000d, 315.53295031801790000000d, 315.53295031801790000000d, 316.75635586418775000000d,
      317.98049266805054000000d, 319.20517848912040000000d, 320.43096382331413000000d, 321.65785064667400000000d,
      322.88547289657800000000d, 324.11419994090970000000d, 324.11419994090970000000d, 324.11419994090970000000d,
      325.34421842797350000000d, 325.34421842797350000000d, 326.57497610189860000000d, 327.80684422343880000000d,
      327.80684422343880000000d, 329.04010322551824000000d, 330.27447719547630000000d, 331.50996815118333000000d,
      332.74657811599235000000d, 332.74657811599235000000d, 333.98393521367100000000d, 335.22143249928140000000d,
      336.46023973901487000000d, 337.69979676987330000000d, 338.94085023368234000000d, 340.18227984019484000000d,
      341.42446241654470000000d, 342.66702182044384000000d, 343.91071308000954000000d, 345.15553825915170000000d,
      346.40149942743040000000d, 347.64859866007690000000d, 348.89645775801813000000d, 350.14545839170450000000d,
      350.14545839170450000000d, 351.39579345960044000000d, 352.64689234234334000000d, 353.89875597371440000000d,
      355.15138528920835000000d, 356.40478122603747000000d, 357.65932885590990000000d, 358.91464545769030000000d,
      360.17063568359646000000d, 361.42797532895287000000d, 362.68647392952226000000d, 363.94613362381415000000d,
      365.20656857157330000000d, 366.46850829169210000000d, 367.73161546672907000000d, 368.99550214583480000000d,
      368.99550214583480000000d, 370.26055988667900000000d, 371.52708450995000000000d, 372.79439286233890000000d,
      374.06317332417296000000d, 375.33274031031710000000d, 376.60378466091320000000d, 377.87561834599194000000d,
      379.14863787270826000000d, 380.42304367925084000000d, 381.69824300211250000000d, 382.97463445401365000000d,
      384.25222026598027000000d, 385.53060356054425000000d, 386.80978533392164000000d, 388.08976658419630000000d,
      389.37094892532167000000d, 390.65333461354050000000d, 391.93692591145900000000d, 391.93692591145900000000d,
      393.22132220933406000000d, 394.50652451750534000000d, 395.79293773967250000000d, 397.08091844040110000000d,
      398.37031821512600000000d, 399.66053029413024000000d, 400.95155570154020000000d, 402.24339546342030000000d,
      403.53543897446810000000d, 404.82829812529934000000d, 404.82829812529934000000d, 406.12258712643000000000d,
      407.41769460576660000000d, 407.41769460576660000000d, 407.41769460576660000000d, 408.71362159913730000000d,
      410.01036914433774000000d, 411.30834946746626000000d, 412.60756491468120000000d, 413.90801783884490000000d,
      415.20867723838944000000d, 416.51078380346150000000d, 416.51078380346150000000d, 417.81454173610120000000d,
      419.11954581822150000000d, 420.42618909120980000000d, 420.42618909120980000000d, 420.42618909120980000000d,
      421.73366654711910000000d, 423.04260638893425000000d, 423.04260638893425000000d, 424.35316912140630000000d,
      424.35316912140630000000d, 425.66520115343840000000d, 426.97881109531050000000d, 426.97881109531050000000d,
      428.29326414196300000000d, 429.60856137633860000000d, 430.92470388346800000000d, 432.24126943451466000000d,
      433.55910575062165000000d, 434.87821528727477000000d, 436.19774977767060000000d, 437.51813499747960000000d,
      438.83979837020576000000d, 440.16231522051050000000d, 441.48632831194850000000d, 442.81204213529050000000d,
      442.81204213529050000000d, 444.13944762226170000000d, 445.46728342576887000000d, 445.46728342576887000000d,
      446.79598069988770000000d, 448.12597227785244000000d, 449.45682812684777000000d, 450.78898249055990000000d,
      452.12200393939895000000d, 453.45589360285317000000d, 454.79108771085280000000d, 456.12780689906350000000d,
      457.46539912692117000000d, 458.80386553557250000000d, 460.14364535996356000000d, 461.48474118029407000000d,
      461.48474118029407000000d, 462.82671576845230000000d, 462.82671576845230000000d, 464.17042380064254000000d,
      465.51501402848180000000d, 466.86037712830216000000d, 468.20662459905530000000d, 469.55453340295490000000d,
      470.90416323089440000000d, 472.25468304996235000000d, 473.60676318117620000000d, 474.96040723409420000000d,
      476.31561883081450000000d, 476.31561883081450000000d, 477.67217692895053000000d, 479.02963418217920000000d,
      480.38730234733015000000d, 481.74587114021557000000d, 483.10621654041483000000d, 484.46791866807440000000d,
      484.46791866807440000000d, 485.83052678517350000000d, 487.19449614914290000000d, 488.56022782088047000000d,
      489.92687085378700000000d, 491.29511169891623000000d, 492.66426725818590000000d, 494.03388063331647000000d,
      495.40509877785340000000d, 496.77769543516500000000d, 498.15167337973290000000d, 498.15167337973290000000d,
      499.52726634392417000000d, 500.90378388225645000000d, 502.28169061452170000000d, 503.66098934752670000000d,
      505.04121764456556000000d, 505.04121764456556000000d, 505.04121764456556000000d, 506.42237675942330000000d,
      507.80516783002290000000d, 509.18889317945917000000d, 509.18889317945917000000d, 510.57402231671244000000d,
      511.96008889596040000000d, 513.34709418696570000000d, 513.34709418696570000000d, 514.73503946207270000000d,
      516.12439710464210000000d, 516.12439710464210000000d, 516.12439710464210000000d, 517.51469792351430000000d,
      517.51469792351430000000d, 517.51469792351430000000d, 517.51469792351430000000d, 518.90677065387670000000d,
      518.90677065387670000000d, 518.90677065387670000000d, 520.30050124806670000000d, 521.69601251249320000000d,
      523.09247532945460000000d, 523.09247532945460000000d, 524.48989099750020000000d, 525.88873838277230000000d,
      527.28830272736720000000d, 528.68882416173910000000d, 530.09030399579240000000d, 531.49346418934350000000d,
      532.89758639871060000000d, 532.89758639871060000000d, 534.30267194392730000000d, 535.70872214774620000000d,
      535.70872214774620000000d, 537.11549671521290000000d, 538.52323826266320000000d, 539.93243277519920000000d,
      541.34259759854130000000d, 541.34259759854130000000d, 541.34259759854130000000d, 542.75373406983870000000d,
      544.16633052627710000000d, 545.58063412159850000000d, 545.58063412159850000000d, 546.99677137904260000000d,
      548.41388853512090000000d, 548.41388853512090000000d, 548.41388853512090000000d, 548.41388853512090000000d,
      549.83149614922430000000d, 551.24959456096100000000d, 552.66867558820100000000d, 552.66867558820100000000d,
      554.08874059361810000000d, 555.50979094272260000000d, 556.93182800386910000000d, 558.35485314826490000000d,
      559.77886774997700000000d, 561.20474129769040000000d, 561.20474129769040000000d, 562.63210550033010000000d,
      564.06046520566120000000d, 565.48982180326210000000d, 566.92067635109850000000d, 568.35228105204650000000d,
      569.78488718154410000000d, 571.21924918635920000000d, 572.65511965654010000000d, 574.09199753419850000000d,
      575.53076811597680000000d, 575.53076811597680000000d, 576.97029717629400000000d, 578.41178934592280000000d,
      579.85518640345070000000d, 581.29947413264680000000d, 582.74452617004320000000d, 584.19110925321470000000d,
      585.63820340619120000000d, 587.08708915079680000000d, 588.53796362500530000000d, 589.98986667786540000000d,
      591.44357325698790000000d, 592.89831243567820000000d, 592.89831243567820000000d, 594.35408568193530000000d,
      594.35408568193530000000d, 595.81089446689070000000d, 597.26874026481740000000d, 598.72710512306660000000d,
      600.18650921160710000000d, 600.18650921160710000000d, 601.64695401260550000000d, 603.10945205996000000000d,
      604.57378006800380000000d, 604.57378006800380000000d, 606.03863176339260000000d, 607.50453195799300000000d,
      608.97148215385200000000d, 608.97148215385200000000d, 608.97148215385200000000d, 608.97148215385200000000d,
      610.44001017500510000000d, 611.91011941926810000000d, 613.38181329544420000000d, 613.38181329544420000000d,
      613.38181329544420000000d, 614.85456549212280000000d, 614.85456549212280000000d, 616.32784742005030000000d,
      617.80159317552030000000d, 617.80159317552030000000d, 619.27719716534320000000d, 620.75466408150080000000d,
      620.75466408150080000000d, 622.23413221704040000000d, 623.71413492700630000000d, 625.19520794560560000000d,
      626.67735282201060000000d, 628.16057110875940000000d, 629.64540242942010000000d, 629.64540242942010000000d,
      629.64540242942010000000d, 629.64540242942010000000d, 631.13131105655990000000d, 632.61775892337470000000d,
      632.61775892337470000000d, 632.61775892337470000000d, 634.10582686007000000000d, 635.59551840190620000000d,
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      2614.57949245417700000000d, 2618.12473668554280000000d, 2621.67266792799860000000d, 2621.67266792799860000000d,
      2625.22367503203800000000d, 2625.22367503203800000000d, 2625.22367503203800000000d, 2625.22367503203800000000d,
      2625.22367503203800000000d, 2628.77930594123500000000d, 2632.33957271270450000000d, 2635.90216195147500000000d,
      2639.46785253079400000000d, 2639.46785253079400000000d, 2639.46785253079400000000d, 2639.46785253079400000000d,
      2639.46785253079400000000d, 2643.03393115738340000000d, 2643.03393115738340000000d, 2646.60623004701900000000d,
      2646.60623004701900000000d, 2646.60623004701900000000d, 2646.60623004701900000000d, 2650.18790012516270000000d,
      2650.18790012516270000000d, 2650.18790012516270000000d, 2650.18790012516270000000d, 2650.18790012516270000000d,
      2650.18790012516270000000d, 2650.18790012516270000000d, 2650.18790012516270000000d, 2650.18790012516270000000d,
      2650.18790012516270000000d, 2650.18790012516270000000d, 2650.18790012516270000000d, 2653.76996173659800000000d,
      2653.76996173659800000000d, 2657.35359033758870000000d, 2657.35359033758870000000d, 2657.35359033758870000000d,
      2657.35359033758870000000d, 2660.93878729970900000000d, 2660.93878729970900000000d, 2660.93878729970900000000d,
      2660.93878729970900000000d, 2660.93878729970900000000d, 2660.93878729970900000000d, 2660.93878729970900000000d,
      2660.93878729970900000000d, 2660.93878729970900000000d, 2660.93878729970900000000d, 2660.93878729970900000000d,
      2660.93878729970900000000d, 2664.53579087158200000000d, 2664.53579087158200000000d, 2668.13432513711450000000d,
      2671.73840052333900000000d, 2675.34287235695730000000d, 2675.34287235695730000000d, 2675.34287235695730000000d,
      2675.34287235695730000000d, 2675.34287235695730000000d, 2678.94972470773400000000d, 2678.94972470773400000000d,
      2678.94972470773400000000d, 2678.94972470773400000000d, 2678.94972470773400000000d, 2678.94972470773400000000d,
      2678.94972470773400000000d, 2678.94972470773400000000d, 2678.94972470773400000000d, 2678.94972470773400000000d,
      2682.55896072209730000000d, 2682.55896072209730000000d, 2682.55896072209730000000d, 2686.17456860275800000000d,
      2686.17456860275800000000d, 2686.17456860275800000000d, 2686.17456860275800000000d, 2686.17456860275800000000d,
      2689.79657088771800000000d, 2689.79657088771800000000d, 2689.79657088771800000000d, 2693.42177886398080000000d,
      2693.42177886398080000000d, 2693.42177886398080000000d, 2693.42177886398080000000d, 2697.05180603095600000000d,
      2697.05180603095600000000d, 2700.68827875201760000000d, 2700.68827875201760000000d, 2700.68827875201760000000d,
      2700.68827875201760000000d, 2700.68827875201760000000d, 2700.68827875201760000000d, 2700.68827875201760000000d,
      2700.68827875201760000000d, 2700.68827875201760000000d, 2700.68827875201760000000d, 2700.68827875201760000000d,
      2700.68827875201760000000d, 2700.68827875201760000000d, 2700.68827875201760000000d, 2704.33041013885350000000d,
      2707.97416152340470000000d, 2707.97416152340470000000d, 2707.97416152340470000000d, 2707.97416152340470000000d,
      2707.97416152340470000000d, 2707.97416152340470000000d, 2711.63010898059600000000d, 2711.63010898059600000000d,
      2711.63010898059600000000d, 2711.63010898059600000000d, 2711.63010898059600000000d, 2715.28646437978000000000d,
      2715.28646437978000000000d, 2718.94854054090300000000d, 2722.61717667513700000000d, 2726.28889589388970000000d,
      2726.28889589388970000000d, 2729.97299944535800000000d, 2729.97299944535800000000d, 2729.97299944535800000000d,
      2729.97299944535800000000d, 2733.65876055610260000000d, 2737.34618071834070000000d, 2741.04025204908750000000d,
      2741.04025204908750000000d, 2741.04025204908750000000d, 2744.73598992272100000000d, 2744.73598992272100000000d,
      2744.73598992272100000000d, 2744.73598992272100000000d, 2748.43506539726400000000d, 2752.14418994283230000000d,
      2752.14418994283230000000d, 2752.14418994283230000000d, 2752.14418994283230000000d, 2752.14418994283230000000d,
      2752.14418994283230000000d, 2752.14418994283230000000d, 2752.14418994283230000000d, 2755.85499464426000000000d,
      2755.85499464426000000000d, 2755.85499464426000000000d, 2755.85499464426000000000d, 2755.85499464426000000000d,
      2755.85499464426000000000d, 2755.85499464426000000000d, 2755.85499464426000000000d, 2759.57591233312900000000d,
      2759.57591233312900000000d, 2759.57591233312900000000d, 2763.30021327816600000000d, 2763.30021327816600000000d,
      2763.30021327816600000000d, 2763.30021327816600000000d, 2763.30021327816600000000d, 2763.30021327816600000000d,
      2763.30021327816600000000d, 2763.30021327816600000000d, 2767.03129922658400000000d, 2767.03129922658400000000d,
      2767.03129922658400000000d, 2767.03129922658400000000d, 2770.76397898783100000000d, 2770.76397898783100000000d,
      2774.50176811302530000000d, 2774.50176811302530000000d, 2774.50176811302530000000d, 2778.24639152174270000000d,
      2781.99441465879140000000d, 2781.99441465879140000000d, 2785.75275494404240000000d, 2785.75275494404240000000d,
      2789.52146933411450000000d, 2789.52146933411450000000d, 2789.52146933411450000000d, 2789.52146933411450000000d,
      2789.52146933411450000000d, 2789.52146933411450000000d, 2789.52146933411450000000d, 2793.30323217147540000000d,
      2797.08848986891700000000d, 2797.08848986891700000000d, 2797.08848986891700000000d, 2797.08848986891700000000d,
      2797.08848986891700000000d, 2800.88691102116600000000d, 2804.69239018735970000000d, 2804.69239018735970000000d,
      2804.69239018735970000000d, 2808.50318010121870000000d, 2808.50318010121870000000d, 2812.32107411273000000000d,
      2816.14609875836640000000d, 2816.14609875836640000000d, 2819.97469871875050000000d, 2819.97469871875050000000d,
      2823.80688068394900000000d, 2823.80688068394900000000d, 2823.80688068394900000000d, 2827.64242687131400000000d,
      2827.64242687131400000000d, 2827.64242687131400000000d, 2831.47976972686230000000d, 2831.47976972686230000000d,
      2831.47976972686230000000d, 2831.47976972686230000000d, 2831.47976972686230000000d, 2831.47976972686230000000d,
      2831.47976972686230000000d, 2831.47976972686230000000d, 2835.31891093459400000000d, 2835.31891093459400000000d,
      2839.16435967070300000000d, 2839.16435967070300000000d, 2839.16435967070300000000d, 2839.16435967070300000000d,
      2839.16435967070300000000d, 2843.01523137913050000000d, 2843.01523137913050000000d, 2843.01523137913050000000d,
      2846.87335755481260000000d, 2850.73876558200300000000d, 2850.73876558200300000000d, 2850.73876558200300000000d,
      2850.73876558200300000000d, 2850.73876558200300000000d, 2850.73876558200300000000d, 2850.73876558200300000000d,
      2850.73876558200300000000d, 2850.73876558200300000000d, 2850.73876558200300000000d, 2854.60554201758030000000d,
      2854.60554201758030000000d, 2854.60554201758030000000d, 2854.60554201758030000000d, 2854.60554201758030000000d,
      2854.60554201758030000000d, 2854.60554201758030000000d, 2854.60554201758030000000d, 2854.60554201758030000000d,
      2854.60554201758030000000d, 2854.60554201758030000000d, 2854.60554201758030000000d, 2854.60554201758030000000d,
      2854.60554201758030000000d, 2854.60554201758030000000d, 2854.60554201758030000000d, 2854.60554201758030000000d,
      2858.47414450551830000000d, 2858.47414450551830000000d, 2858.47414450551830000000d, 2858.47414450551830000000d,
      2858.47414450551830000000d, 2862.35649755559200000000d, 2862.35649755559200000000d, 2862.35649755559200000000d,
      2866.24992163607600000000d, 2870.14427115321720000000d, 2874.05162313129900000000d, 2874.05162313129900000000d,
      2874.05162313129900000000d, 2874.05162313129900000000d, 2877.96550895377600000000d, 2877.96550895377600000000d,
      2881.88220168936960000000d, 2885.80029939183440000000d, 2885.80029939183440000000d, 2885.80029939183440000000d,
      2885.80029939183440000000d, 2885.80029939183440000000d, 2885.80029939183440000000d, 2889.72003749679600000000d,
      2889.72003749679600000000d, 2889.72003749679600000000d, 2889.72003749679600000000d, 2889.72003749679600000000d,
      2889.72003749679600000000d, 2889.72003749679600000000d, 2889.72003749679600000000d, 2889.72003749679600000000d,
      2893.64118275469500000000d, 2893.64118275469500000000d, 2893.64118275469500000000d, 2897.56937895921240000000d,
      2897.56937895921240000000d, 2897.56937895921240000000d, 2897.56937895921240000000d, 2897.56937895921240000000d,
      2897.56937895921240000000d, 2901.50323420495700000000d, 2901.50323420495700000000d, 2905.43992509012300000000d,
      2905.43992509012300000000d, 2905.43992509012300000000d, 2905.43992509012300000000d, 2909.37732552401300000000d,
      2913.31851454172830000000d, 2913.31851454172830000000d, 2913.31851454172830000000d, 2913.31851454172830000000d,
      2913.31851454172830000000d, 2913.31851454172830000000d, 2913.31851454172830000000d, 2913.31851454172830000000d,
      2913.31851454172830000000d, 2913.31851454172830000000d, 2913.31851454172830000000d, 2913.31851454172830000000d,
      2913.31851454172830000000d, 2913.31851454172830000000d, 2917.26349944107460000000d, 2917.26349944107460000000d,
      2921.21228754096400000000d, 2921.21228754096400000000d, 2925.16393285704000000000d, 2925.16393285704000000000d,
      2925.16393285704000000000d, 2925.16393285704000000000d, 2929.11843952707570000000d, 2929.11843952707570000000d,
      2929.11843952707570000000d, 2933.07390090282400000000d, 2933.07390090282400000000d, 2933.07390090282400000000d,
      2933.07390090282400000000d, 2933.07390090282400000000d, 2933.07390090282400000000d, 2933.07390090282400000000d,
      2933.07390090282400000000d, 2937.03127307358800000000d, 2937.03127307358800000000d, 2937.03127307358800000000d,
      2937.03127307358800000000d, 2937.03127307358800000000d, 2937.03127307358800000000d, 2937.03127307358800000000d,
      2940.99534758976320000000d, 2940.99534758976320000000d, 2940.99534758976320000000d, 2940.99534758976320000000d,
      2940.99534758976320000000d, 2944.96710978235020000000d, 2944.96710978235020000000d, 2944.96710978235020000000d,
      2944.96710978235020000000d, 2944.96710978235020000000d, 2944.96710978235020000000d, 2944.96710978235020000000d,
      2944.96710978235020000000d, 2948.94465732880600000000d, 2952.92413707373540000000d, 2956.90506719990300000000d,
      2956.90506719990300000000d, 2960.90129040432930000000d, 2960.90129040432930000000d, 2960.90129040432930000000d,
      2960.90129040432930000000d, 2960.90129040432930000000d, 2960.90129040432930000000d, 2960.90129040432930000000d,
      2964.90532660796860000000d, 2964.90532660796860000000d, 2964.90532660796860000000d, 2964.90532660796860000000d,
      2964.90532660796860000000d, 2964.90532660796860000000d, 2964.90532660796860000000d, 2964.90532660796860000000d,
      2964.90532660796860000000d, 2964.90532660796860000000d, 2964.90532660796860000000d, 2968.91034158510400000000d,
      2968.91034158510400000000d, 2972.91927644606800000000d, 2972.91927644606800000000d, 2972.91927644606800000000d,
      2972.91927644606800000000d, 2976.93213887150200000000d, 2980.94696796647000000000d, 2984.96968305439440000000d,
      2989.00428539013860000000d, 2989.00428539013860000000d, 2993.03975725308500000000d, 2997.07920887515300000000d,
      2997.07920887515300000000d, 2997.07920887515300000000d, 2997.07920887515300000000d, 2997.07920887515300000000d,
      3001.12564399651300000000d, 3001.12564399651300000000d, 3001.12564399651300000000d, 3005.17583022011880000000d,
      3005.17583022011880000000d, 3005.17583022011880000000d, 3005.17583022011880000000d, 3005.17583022011880000000d,
      3005.17583022011880000000d, 3009.22701791251000000000d, 3009.22701791251000000000d, 3009.22701791251000000000d,
      3009.22701791251000000000d, 3009.22701791251000000000d, 3013.28121298499950000000d, 3013.28121298499950000000d,
      3017.33738407841340000000d, 3021.39757588291880000000d, 3025.46482314567770000000d, 3029.53915043013240000000d,
      3029.53915043013240000000d, 3029.53915043013240000000d, 3029.53915043013240000000d, 3029.53915043013240000000d,
      3029.53915043013240000000d, 3033.61956595248800000000d, 3033.61956595248800000000d, 3033.61956595248800000000d,
      3033.61956595248800000000d, 3033.61956595248800000000d, 3033.61956595248800000000d, 3033.61956595248800000000d,
      3033.61956595248800000000d, 3033.61956595248800000000d, 3033.61956595248800000000d, 3037.71221269992840000000d,
      3037.71221269992840000000d, 3041.80895283364400000000d, 3041.80895283364400000000d, 3041.80895283364400000000d,
      3041.80895283364400000000d, 3045.91802240355540000000d, 3045.91802240355540000000d, 3050.02805833681600000000d,
      3054.14532417570440000000d, 3054.14532417570440000000d, 3054.14532417570440000000d, 3054.14532417570440000000d,
      3054.14532417570440000000d, 3054.14532417570440000000d, 3054.14532417570440000000d, 3054.14532417570440000000d,
      3054.14532417570440000000d, 3058.26284869597480000000d, 3058.26284869597480000000d, 3062.38762951526540000000d,
      3066.51656828559230000000d, 3070.64758917656350000000d, 3070.64758917656350000000d, 3070.64758917656350000000d
  };

  private static final double[] inversePow2Vals = new double[]{
      1023.12500000000000000000d, 1022.62500000000000000000d, 1022.12500000000000000000d, 1021.37500000000000000000d,
      1020.87500000000000000000d, 1020.12500000000000000000d, 1019.25000000000000000000d, 1018.37500000000000000000d,
      1017.87500000000000000000d, 1017.37500000000000000000d, 1016.87500000000000000000d, 1016.37500000000000000000d,
      1015.87500000000000000000d, 1015.12500000000000000000d, 1014.62500000000000000000d, 1013.87500000000000000000d,
      1013.12500000000000000000d, 1012.25000000000000000000d, 1011.75000000000000000000d, 1011.00000000000000000000d,
      1010.50000000000000000000d, 1010.00000000000000000000d, 1009.50000000000000000000d, 1008.75000000000000000000d,
      1008.00000000000000000000d, 1007.50000000000000000000d, 1006.62500000000000000000d, 1005.87500000000000000000d,
      1005.12500000000000000000d, 1004.37500000000000000000d, 1003.62500000000000000000d, 1003.12500000000000000000d,
      1002.62500000000000000000d, 1002.12500000000000000000d, 1001.62500000000000000000d, 1001.12500000000000000000d,
      1001.00000000000000000000d, 1000.25000000000000000000d, 999.75000000000000000000d, 999.25000000000000000000d,
      998.50000000000000000000d, 998.50000000000000000000d, 997.75000000000000000000d, 996.81250000000000000000d,
      996.31250000000000000000d, 995.43750000000000000000d, 994.93750000000000000000d, 994.18750000000000000000d,
      993.68750000000000000000d, 992.93750000000000000000d, 992.43750000000000000000d, 991.93750000000000000000d,
      991.43750000000000000000d, 990.68750000000000000000d, 990.18750000000000000000d, 989.68750000000000000000d,
      989.18750000000000000000d, 988.68750000000000000000d, 988.18750000000000000000d, 987.43750000000000000000d,
      986.68750000000000000000d, 985.71875000000000000000d, 985.21875000000000000000d, 984.34375000000000000000d,
      983.84375000000000000000d, 983.09375000000000000000d, 982.21875000000000000000d, 981.71875000000000000000d,
      980.84375000000000000000d, 980.09375000000000000000d, 979.34375000000000000000d, 978.84375000000000000000d,
      978.09375000000000000000d, 977.59375000000000000000d, 976.84375000000000000000d, 976.09375000000000000000d,
      975.59375000000000000000d, 975.09375000000000000000d, 974.21875000000000000000d, 973.71875000000000000000d,
      972.84375000000000000000d, 972.34375000000000000000d, 971.40625000000000000000d, 970.53125000000000000000d,
      969.65625000000000000000d, 968.67187500000000000000d, 968.67187500000000000000d, 967.92187500000000000000d,
      967.04687500000000000000d, 966.10937500000000000000d, 965.60937500000000000000d, 965.35937500000000000000d,
      964.60937500000000000000d, 964.10937500000000000000d, 963.17187500000000000000d, 962.67187500000000000000d,
      961.92187500000000000000d, 961.42187500000000000000d, 960.67187500000000000000d, 960.17187500000000000000d,
      959.67187500000000000000d, 959.17187500000000000000d, 958.42187500000000000000d, 957.92187500000000000000d,
      957.42187500000000000000d, 956.67187500000000000000d, 956.67187500000000000000d, 955.79687500000000000000d,
      955.04687500000000000000d, 954.54687500000000000000d, 953.67187500000000000000d, 952.79687500000000000000d,
      951.92187500000000000000d, 951.04687500000000000000d, 950.07812500000000000000d, 949.59375000000000000000d,
      949.59375000000000000000d, 949.59375000000000000000d, 948.71875000000000000000d, 948.21875000000000000000d,
      947.71875000000000000000d, 947.21875000000000000000d, 946.71875000000000000000d, 945.96875000000000000000d,
      945.46875000000000000000d, 944.96875000000000000000d, 944.46875000000000000000d, 943.96875000000000000000d,
      943.46875000000000000000d, 942.96875000000000000000d, 942.46875000000000000000d, 941.96875000000000000000d,
      941.21875000000000000000d, 940.71875000000000000000d, 939.78125000000000000000d, 938.81250000000000000000d,
      938.31250000000000000000d, 937.81250000000000000000d, 937.31250000000000000000d, 936.81250000000000000000d,
      936.31250000000000000000d, 935.56250000000000000000d, 935.37500000000000000000d, 934.87500000000000000000d,
      934.00000000000000000000d, 933.25000000000000000000d, 932.75000000000000000000d, 931.81250000000000000000d,
      930.93750000000000000000d, 930.06250000000000000000d, 929.31250000000000000000d, 928.81250000000000000000d,
      927.93750000000000000000d, 927.43750000000000000000d, 926.68750000000000000000d, 926.68750000000000000000d,
      926.68750000000000000000d, 925.93750000000000000000d, 925.43750000000000000000d, 924.50000000000000000000d,
      923.75000000000000000000d, 923.00000000000000000000d, 922.50000000000000000000d, 922.00000000000000000000d,
      921.50000000000000000000d, 921.03125000000000000000d, 920.53125000000000000000d, 920.03125000000000000000d,
      919.28125000000000000000d, 918.53125000000000000000d, 918.03125000000000000000d, 917.78125000000000000000d,
      917.03125000000000000000d, 916.15625000000000000000d, 915.65625000000000000000d, 915.15625000000000000000d,
      914.40625000000000000000d, 913.53125000000000000000d, 912.59375000000000000000d, 911.71875000000000000000d,
      911.71875000000000000000d, 911.21875000000000000000d, 910.25000000000000000000d, 909.75000000000000000000d,
      909.00000000000000000000d, 908.50000000000000000000d, 908.00000000000000000000d, 907.75000000000000000000d,
      907.00000000000000000000d, 906.25000000000000000000d, 905.37500000000000000000d, 904.43750000000000000000d,
      903.56250000000000000000d, 903.56250000000000000000d, 903.06250000000000000000d, 902.12500000000000000000d,
      901.14062500000000000000d, 900.17187500000000000000d, 899.42187500000000000000d, 898.48437500000000000000d,
      897.54687500000000000000d, 897.04687500000000000000d, 897.04687500000000000000d, 896.54687500000000000000d,
      896.54687500000000000000d, 896.04687500000000000000d, 896.04687500000000000000d, 895.17187500000000000000d,
      894.23437500000000000000d, 893.98437500000000000000d, 893.48437500000000000000d, 892.54687500000000000000d,
      892.54687500000000000000d, 891.67187500000000000000d, 891.17187500000000000000d, 890.67187500000000000000d,
      890.17187500000000000000d, 889.42187500000000000000d, 889.42187500000000000000d, 888.92187500000000000000d,
      887.98437500000000000000d, 887.76562500000000000000d, 887.26562500000000000000d, 886.76562500000000000000d,
      886.26562500000000000000d, 885.32812500000000000000d, 884.82812500000000000000d, 884.32812500000000000000d,
      883.82812500000000000000d, 883.07812500000000000000d, 882.10937500000000000000d, 881.60937500000000000000d,
      880.67187500000000000000d, 880.55468750000000000000d, 880.05468750000000000000d, 879.55468750000000000000d,
      879.05468750000000000000d, 879.05468750000000000000d, 878.30468750000000000000d, 877.42968750000000000000d,
      877.17968750000000000000d, 876.24218750000000000000d, 875.30468750000000000000d, 874.80468750000000000000d,
      874.30468750000000000000d, 873.80468750000000000000d, 873.80468750000000000000d, 872.92968750000000000000d,
      871.99218750000000000000d, 871.49218750000000000000d, 870.99218750000000000000d, 870.05468750000000000000d,
      869.30468750000000000000d, 868.80468750000000000000d, 868.05468750000000000000d, 867.17968750000000000000d,
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