Source: quadrature.js

/**
 * A port of Boost's Gauss-Kronrod and double exponential quadrature procedures. Original license header is:
 *
 *   Copyright John Maddock 2017.
 *   Copyright Nick Thompson 2017.
 *   Use, modification and distribution are subject to the
 *   Boost Software License, Version 1.0. (See accompanying file
 *   LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
 *
 * @module quadrature
 * @license Boost
 */

const GAUSS_KRONROD_ABSCISSA = {
  21: [
    0.00000000000000000000000000000000000e+00,
    1.48874338981631210884826001129719985e-01,
    2.94392862701460198131126603103865566e-01,
    4.33395394129247190799265943165784162e-01,
    5.62757134668604683339000099272694141e-01,
    6.79409568299024406234327365114873576e-01,
    7.80817726586416897063717578345042377e-01,
    8.65063366688984510732096688423493049e-01,
    9.30157491355708226001207180059508346e-01,
    9.73906528517171720077964012084452053e-01,
    9.95657163025808080735527280689002848e-01,
  ],
  31: [
    0.00000000000000000000000000000000000e+00,
    1.01142066918717499027074231447392339e-01,
    2.01194093997434522300628303394596208e-01,
    2.99180007153168812166780024266388963e-01,
    3.94151347077563369897207370981045468e-01,
    4.85081863640239680693655740232350613e-01,
    5.70972172608538847537226737253910641e-01,
    6.50996741297416970533735895313274693e-01,
    7.24417731360170047416186054613938010e-01,
    7.90418501442465932967649294817947347e-01,
    8.48206583410427216200648320774216851e-01,
    8.97264532344081900882509656454495883e-01,
    9.37273392400705904307758947710209471e-01,
    9.67739075679139134257347978784337225e-01,
    9.87992518020485428489565718586612581e-01,
    9.98002298693397060285172840152271209e-01,
  ],
  61: [
    0.00000000000000000000000000000000000e+00,
    5.14718425553176958330252131667225737e-02,
    1.02806937966737030147096751318000592e-01,
    1.53869913608583546963794672743255920e-01,
    2.04525116682309891438957671002024710e-01,
    2.54636926167889846439805129817805108e-01,
    3.04073202273625077372677107199256554e-01,
    3.52704725530878113471037207089373861e-01,
    4.00401254830394392535476211542660634e-01,
    4.47033769538089176780609900322854000e-01,
    4.92480467861778574993693061207708796e-01,
    5.36624148142019899264169793311072794e-01,
    5.79345235826361691756024932172540496e-01,
    6.20526182989242861140477556431189299e-01,
    6.60061064126626961370053668149270753e-01,
    6.97850494793315796932292388026640068e-01,
    7.33790062453226804726171131369527646e-01,
    7.67777432104826194917977340974503132e-01,
    7.99727835821839083013668942322683241e-01,
    8.29565762382768397442898119732501916e-01,
    8.57205233546061098958658510658943857e-01,
    8.82560535792052681543116462530225590e-01,
    9.05573307699907798546522558925958320e-01,
    9.26200047429274325879324277080474004e-01,
    9.44374444748559979415831324037439122e-01,
    9.60021864968307512216871025581797663e-01,
    9.73116322501126268374693868423706885e-01,
    9.83668123279747209970032581605662802e-01,
    9.91630996870404594858628366109485725e-01,
    9.96893484074649540271630050918695283e-01,
    9.99484410050490637571325895705810819e-01,
  ],
};

const GAUSS_KRONROD_WEIGHTS = {
  21: [
    1.49445554002916905664936468389821204e-01,
    1.47739104901338491374841515972068046e-01,
    1.42775938577060080797094273138717061e-01,
    1.34709217311473325928054001771706833e-01,
    1.23491976262065851077958109831074160e-01,
    1.09387158802297641899210590325804960e-01,
    9.31254545836976055350654650833663444e-02,
    7.50396748109199527670431409161900094e-02,
    5.47558965743519960313813002445801764e-02,
    3.25581623079647274788189724593897606e-02,
    1.16946388673718742780643960621920484e-02,
  ],
  31: [
    1.01330007014791549017374792767492547e-01,
    1.00769845523875595044946662617569722e-01,
    9.91735987217919593323931734846031311e-02,
    9.66427269836236785051799076275893351e-02,
    9.31265981708253212254868727473457186e-02,
    8.85644430562117706472754436937743032e-02,
    8.30805028231330210382892472861037896e-02,
    7.68496807577203788944327774826590067e-02,
    6.98541213187282587095200770991474758e-02,
    6.20095678006706402851392309608029322e-02,
    5.34815246909280872653431472394302968e-02,
    4.45897513247648766082272993732796902e-02,
    3.53463607913758462220379484783600481e-02,
    2.54608473267153201868740010196533594e-02,
    1.50079473293161225383747630758072681e-02,
    5.37747987292334898779205143012764982e-03,
  ],
  61: [
    5.14947294294515675583404336470993075e-02,
    5.14261285374590259338628792157812598e-02,
    5.12215478492587721706562826049442083e-02,
    5.08817958987496064922974730498046919e-02,
    5.04059214027823468408930856535850289e-02,
    4.97956834270742063578115693799423285e-02,
    4.90554345550297788875281653672381736e-02,
    4.81858617570871291407794922983045926e-02,
    4.71855465692991539452614781810994865e-02,
    4.60592382710069881162717355593735806e-02,
    4.48148001331626631923555516167232438e-02,
    4.34525397013560693168317281170732581e-02,
    4.19698102151642461471475412859697578e-02,
    4.03745389515359591119952797524681142e-02,
    3.86789456247275929503486515322810503e-02,
    3.68823646518212292239110656171359677e-02,
    3.49793380280600241374996707314678751e-02,
    3.29814470574837260318141910168539275e-02,
    3.09072575623877624728842529430922726e-02,
    2.87540487650412928439787853543342111e-02,
    2.65099548823331016106017093350754144e-02,
    2.41911620780806013656863707252320268e-02,
    2.18280358216091922971674857383389934e-02,
    1.94141411939423811734089510501284559e-02,
    1.69208891890532726275722894203220924e-02,
    1.43697295070458048124514324435800102e-02,
    1.18230152534963417422328988532505929e-02,
    9.27327965951776342844114689202436042e-03,
    6.63070391593129217331982636975016813e-03,
    3.89046112709988405126720184451550328e-03,
    1.38901369867700762455159122675969968e-03,
  ],
};

// const GAUSS_ABSCISSA = {
//   10: [
//     1.48874338981631210884826001129719985e-01,
//     4.33395394129247190799265943165784162e-01,
//     6.79409568299024406234327365114873576e-01,
//     8.65063366688984510732096688423493049e-01,
//     9.73906528517171720077964012084452053e-01
//   ],
//   15: [
//     0.00000000000000000000000000000000000e+00,
//     2.01194093997434522300628303394596208e-01,
//     3.94151347077563369897207370981045468e-01,
//     5.70972172608538847537226737253910641e-01,
//     7.24417731360170047416186054613938010e-01,
//     8.48206583410427216200648320774216851e-01,
//     9.37273392400705904307758947710209471e-01,
//     9.87992518020485428489565718586612581e-01,
//   ],
//   30: [
//     5.14718425553176958330252131667225737e-02,
//     1.53869913608583546963794672743255920e-01,
//     2.54636926167889846439805129817805108e-01,
//     3.52704725530878113471037207089373861e-01,
//     4.47033769538089176780609900322854000e-01,
//     5.36624148142019899264169793311072794e-01,
//     6.20526182989242861140477556431189299e-01,
//     6.97850494793315796932292388026640068e-01,
//     7.67777432104826194917977340974503132e-01,
//     8.29565762382768397442898119732501916e-01,
//     8.82560535792052681543116462530225590e-01,
//     9.26200047429274325879324277080474004e-01,
//     9.60021864968307512216871025581797663e-01,
//     9.83668123279747209970032581605662802e-01,
//     9.96893484074649540271630050918695283e-01,
//   ]
// };

const GAUSS_WEIGHTS = {
  10: [
    2.95524224714752870173892994651338329e-01,
    2.69266719309996355091226921569469353e-01,
    2.19086362515982043995534934228163192e-01,
    1.49451349150580593145776339657697332e-01,
    6.66713443086881375935688098933317929e-02,
  ],
  15: [
    2.02578241925561272880620199967519315e-01,
    1.98431485327111576456118326443839325e-01,
    1.86161000015562211026800561866422825e-01,
    1.66269205816993933553200860481208811e-01,
    1.39570677926154314447804794511028323e-01,
    1.07159220467171935011869546685869303e-01,
    7.03660474881081247092674164506673385e-02,
    3.07532419961172683546283935772044177e-02,
  ],
  30: [
    1.02852652893558840341285636705415044e-01,
    1.01762389748405504596428952168554045e-01,
    9.95934205867952670627802821035694765e-02,
    9.63687371746442596394686263518098651e-02,
    9.21225222377861287176327070876187672e-02,
    8.68997872010829798023875307151257026e-02,
    8.07558952294202153546949384605297309e-02,
    7.37559747377052062682438500221907342e-02,
    6.59742298821804951281285151159623612e-02,
    5.74931562176190664817216894020561288e-02,
    4.84026728305940529029381404228075178e-02,
    3.87991925696270495968019364463476920e-02,
    2.87847078833233693497191796112920436e-02,
    1.84664683110909591423021319120472691e-02,
    7.96819249616660561546588347467362245e-03,
  ],
};

const ROOT_EPSILON = Math.sqrt(Number.EPSILON);

class GaussKronrod {
  constructor(N = 21, maxDepth = 15, maxRelativeError = ROOT_EPSILON) {
    this.N = N;
    this.maxDepth = maxDepth;
    this.maxRelativeError = maxRelativeError;
    this.error = 0;
  }

  _integrateNonAdaptive(f) {
    let N = this.N;
    let gauss_start = 2;
    let kronrod_start = 1;
    let gauss_order = (N - 1) / 2;
    let kronrod_result = 0;
    let gauss_result = 0;
    let fp, fm;

    if (gauss_order & 1) {
      fp = f(0);
      kronrod_result = fp * GAUSS_KRONROD_WEIGHTS[N][0];
      gauss_result += fp * GAUSS_WEIGHTS[(N - 1) / 2][0];
    } else {
      fp = f(0);
      kronrod_result = fp * GAUSS_KRONROD_WEIGHTS[N][0];
      gauss_start = 1;
      kronrod_start = 2;
    }

    for (let i = gauss_start; i < GAUSS_KRONROD_ABSCISSA[N].length; i += 2) {
      fp = f(GAUSS_KRONROD_ABSCISSA[N][i]);
      fm = f(-GAUSS_KRONROD_ABSCISSA[N][i]);
      kronrod_result += (fp + fm) * GAUSS_KRONROD_WEIGHTS[N][i];
      gauss_result += (fp + fm) * GAUSS_WEIGHTS[(N - 1) / 2][Math.floor(i / 2)];
    }

    for (let i = kronrod_start; i < GAUSS_KRONROD_ABSCISSA[N].length; i += 2) {
      fp = f(GAUSS_KRONROD_ABSCISSA[N][i]);
      fm = f(-GAUSS_KRONROD_ABSCISSA[N][i]);
      kronrod_result += (fp + fm) * GAUSS_KRONROD_WEIGHTS[N][i];
    }

    let error = Math.max(Math.abs(kronrod_result - gauss_result), Math.abs(kronrod_result * Number.EPSILON * 2));
    return [kronrod_result, error];
  }

  _recursiveAdaptiveIntegrate(f, a, b, max_levels, abs_tol) {
    let error_local;
    let estimate;
    let mean = (b + a) / 2;
    let scale = (b - a) / 2;
    let ff = (x) => {
      return f(scale * x + mean);
    };
    [estimate, error_local] = this._integrateNonAdaptive(ff);
    estimate *= scale;

    let abs_tol1 = Math.abs(estimate * this.maxRelativeError);
    if (!abs_tol) {
      abs_tol = abs_tol1;
    }

    if (max_levels && (abs_tol < error_local)) {
      let mid = (a + b) / 2;
      [estimate ] = this._recursiveAdaptiveIntegrate(f, a, mid, max_levels - 1, abs_tol / 2);
      let result = this._recursiveAdaptiveIntegrate(f, mid, b, max_levels - 1, abs_tol / 2);
      estimate += result[0];
      this.error += result[1];
      return [estimate, error_local];
    }

    this.error = error_local;
    //let dbg = `${a.toString().padEnd(15)} ${b.toString().padEnd(15)} ${max_levels.toString().padEnd(5)} ${abs_tol.toExponential(2).padEnd(11)} ${estimate.toExponential(2).padEnd(11)} ${error_local.toExponential(2).padStart(5).padEnd(11)}\n`;
    //this.stream.write(dbg);
    return [estimate, error_local];
  }

  integrate(f, a, b) {
    let result;
    if (isFinite(a) && isFinite(b)) {
      result = this._recursiveAdaptiveIntegrate(f, a, b, this.maxDepth, 0);
    } else {
      throw new Error('Additional integration limits not implemented');
    }
    return result;
  }
}

const EXP_SINH_ABSCISSAS = [
  [7.241670621354483269e-163, 2.257639733856759198e-60, 1.153241619257215165e-22, 8.747691973876861825e-09, 1.173446923800022477e-03, 1.032756936219208144e-01, 7.719261204224504866e-01, 4.355544675823585545e+00, 1.215101039066652656e+02, 6.228845436711506169e+05, 6.278613977336989392e+15, 9.127414935180233465e+42, 6.091127771174027909e+116],
  [4.547459836328942014e-99, 6.678756542928857080e-37, 5.005042973041566360e-14, 1.341318484151208960e-05, 1.833875636365939263e-02, 3.257972971286326131e-01, 1.712014688483495078e+00, 1.613222549264089627e+01, 3.116246745274236447e+03, 3.751603952020919663e+09, 1.132259067258797346e+26, 6.799257464097374238e+70],
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  [8.165631636299519857e-144, 3.658949309353149331e-112, 1.635242513882908826e-87, 2.578381184977746454e-68, 2.305546416275824199e-53, 1.016725540031465162e-41, 1.191823622917539774e-32, 1.379018088205016509e-25, 4.375640088826073184e-20, 8.438464631330991606e-16, 1.838483310261119782e-12, 7.334264181393092650e-10, 7.804740587931068021e-08, 2.970395577741681504e-06, 5.081805431666579484e-05, 4.671401627620431498e-04, 2.652347404231090523e-03, 1.037409202661683856e-02, 3.045225582205323946e-02, 7.178280364982721201e-02, 1.434001065841990688e-01, 2.535640852949085796e-01, 4.113268917643175920e-01, 6.310260805648534613e-01, 9.404706503455087817e-01, 1.396267301972783068e+00, 2.116896928689963277e+00, 3.364289290471596568e+00, 5.770183960005836987e+00, 1.104863531218761752e+01, 2.460224479439805859e+01, 6.699316387888639988e+01, 2.375794092475844708e+02, 1.188092202760116066e+03, 9.269848635975416108e+03, 1.283900116155671304e+05, 3.723397798030112514e+06, 2.793667983952389721e+08, 7.112973790863854188e+10, 8.704037695808749572e+13, 8.001474015782459984e+17, 9.804091819390540578e+22, 3.342777673392873288e+29, 8.160092668471508447e+37, 4.798775331663586528e+48, 3.228614320248853938e+62, 1.836986041572136151e+80, 1.153145986877483804e+103, 2.160972586723647751e+132],
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4.661192830883879903e-02, 4.917131958110712872e-02, 5.183310721786459418e-02, 5.459951712697841302e-02, 5.747275949639657337e-02, 6.045502790319455825e-02, 6.354849857288828754e-02, 6.675532979350985865e-02, 7.007766148848641979e-02, 7.351761495191403887e-02, 7.707729274938041525e-02, 8.075877878706524317e-02, 8.456413855143733669e-02, 8.849541952147546057e-02, 9.255465175496720496e-02, 9.674384865008904765e-02, 1.010650078831426502e-01, 1.055201125230189472e-01, 1.101111323226840632e-01, 1.148400251877307103e-01, 1.197087388218165293e-01, 1.247192125486176994e-01, 1.298733793097628269e-01, 1.351731678380792159e-01, 1.406205050053816316e-01, 1.462173183439629526e-01, 1.519655387409069424e-01, 1.578671033043359383e-01, 1.639239584007306411e-01, 1.701380628625154331e-01, 1.765113913651907042e-01, 1.830459379734134606e-01, 1.897437198555789051e-01, 1.966067811666385690e-01, 2.036371970991047974e-01, 2.108370781024367852e-01, 2.182085742712797843e-01, 2.257538799033364379e-01, 2.334752382279873511e-01, 2.413749463071469410e-01, 2.494553601102403241e-01, 2.577188997656175820e-01, 2.661680549911833443e-01, 2.748053907075124803e-01, 2.836335528372471376e-01, 2.926552742951268547e-01, 3.018733811735925662e-01, 3.112907991295277084e-01, 3.209105599783561596e-01, 3.307358085024083972e-01, 3.407698094811951648e-01, 3.510159549519934555e-01, 3.614777717099542274e-01, 3.721589290577866932e-01, 3.830632468159621812e-01, 3.941947036053136035e-01, 4.055574454148868711e-01, 4.171557944689308074e-01, 4.289942584079951543e-01, 4.410775398002453309e-01, 4.534105460003012245e-01, 4.659983993741692944e-01, 4.788464479101668631e-01, 4.919602762371392109e-01, 5.053457170727489659e-01, 5.190088631261786795e-01, 5.329560794812372669e-01, 5.471940164876055195e-01, 5.617296231898020413e-01, 5.765701613254061793e-01, 5.917232199261468491e-01, 6.071967305576643327e-01, 6.229989832360855492e-01, 6.391386430620321596e-01, 6.556247676153161584e-01, 6.724668251563812272e-01, 6.896747136835329047e-01, 7.072587808981804764e-01, 7.252298451337033758e-01, 7.435992173071710726e-01, 7.623787239570054101e-01, 7.815807314337971290e-01, 8.012181713158943859e-01, 8.213045671260926392e-01, 8.418540624307963733e-01, 8.628814504084197628e-01, 8.844022049795737430e-01, 9.064325135977815717e-01, 9.289893118061069464e-01, 9.520903196722039764e-01, 9.757540802219457353e-01, 1.000000000000000000e+00, 1.024848391894543008e+00, 1.050320520372784475e+00, 1.076438649284173871e+00, 1.103226092399127978e+00, 1.130707266862927052e+00, 1.158907749757141229e+00, 1.187854337974646084e+00, 1.217575111629048984e+00, 1.248099501235266386e+00, 1.279458358915164500e+00, 1.311684033900709062e+00, 1.344810452627081143e+00, 1.378873203729832710e+00, 1.413909628283517352e+00, 1.449958915644490754e+00, 1.487062205287898607e+00, 1.525262695058439148e+00, 1.564605756286502811e+00, 1.605139056255971231e+00, 1.646912688547541313e+00, 1.689979311822189937e+00, 1.734394297653598793e+00, 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7.257952842284018994e+02, 8.074558443729566627e+02, 8.997734679339701200e+02, 1.004312392957944252e+03, 1.122890361185594877e+03, 1.257623408459775530e+03, 1.410979202907522234e+03, 1.585840680166573460e+03, 1.785582106601447262e+03, 2.014160171499825914e+03, 2.276223289283167479e+03, 2.577243010007973485e+03, 2.923672325162804598e+03, 3.323136759290736047e+03, 3.784665511113575050e+03, 4.318971620160236406e+03, 4.938792274850918489e+03, 5.659303058273368331e+03, 6.498623292476395004e+03, 7.478433875318933386e+03, 8.624734342286166238e+03, 9.968772633484590145e+03, 1.154818959559393902e+04, 1.340843110702649390e+04, 1.560449453908580443e+04, 1.820309391023133793e+04, 2.128535066649680777e+04, 2.495014598048375046e+04, 2.931830770482188047e+04, 3.453785313845473397e+04, 4.079057084931056631e+04, 4.830030527863206410e+04, 5.734341246586992004e+04, 6.826199159022146453e+04, 8.148067525594191464e+04, 9.752799507478730867e+04, 1.170636462204808295e+05, 1.409133795481584143e+05, 1.701137853111825512e+05, 2.059699426710509940e+05, 2.501298539735692463e+05, 3.046808435555379486e+05, 3.722747886360361411e+05, 4.562913164460176067e+05, 5.610511554921845541e+05, 6.920959565810343691e+05, 8.565564972181198149e+05, 1.063638800552326000e+06, 1.325268101226286025e+06, 1.656944841847240121e+06, 2.078886479301160156e+06, 2.617555920130068069e+06, 3.307714852226224955e+06, 4.195192293202626259e+06, 5.340631300250745566e+06, 6.824578495767020734e+06, 8.754424053248831818e+06, 1.127390159772263517e+07, 1.457614342739689625e+07, 1.892169326841938100e+07, 2.466345986800667442e+07, 3.228142821711217588e+07, 4.243114571539869754e+07, 5.601173714434088431e+07, 7.426172509723072112e+07, 9.889461357830121731e+07, 1.322915875470427182e+08, 1.777766240727455981e+08, 2.400110583389834263e+08, 3.255621033641982742e+08, 4.437258820593761403e+08, 6.077246218504877165e+08, 8.364565879857375417e+08, 1.157066594326456169e+09, 1.608740826498742961e+09, 2.248337657948688269e+09, 3.158785978851336228e+09, 4.461677081363911380e+09, 6.336244831048209270e+09, 9.048130159588677560e+09, 1.299321362309972265e+10, 1.876478261212947929e+10, 2.725703976712888971e+10, 3.982553459064288940e+10, 5.853727794017415415e+10, 8.656299089553103385e+10, 1.287959733041898747e+11, 1.928345065430099883e+11, 2.905510467545806044e+11, 4.406145488098485809e+11, 6.725708918778493152e+11, 1.033486938212196930e+12, 1.598840557086695854e+12, 2.490490134218272825e+12, 3.906528466724583921e+12, 6.171225147961354244e+12, 9.819163736485109137e+12, 1.573800106991564475e+13, 2.541245461530031221e+13, 4.134437628407981776e+13, 6.778141973485971528e+13, 1.119906286595884492e+14, 1.865016806041768967e+14, 3.130890948724989738e+14, 5.298978847669068280e+14, 9.042973899804181753e+14, 1.556259036818991439e+15, 2.701230066368200812e+15, 4.729430105054711279e+15, 8.353779033096586530e+15, 1.488827606293191651e+16, 2.677653466031614956e+16, 4.860434481369499270e+16, 8.905735519300993312e+16, 1.647413728306871552e+17, 3.077081325673016377e+17, 5.804234101329097680e+17, 1.105828570628099614e+18, 2.128315358808074026e+18, 4.138651532085235581e+18, 8.132554212123920035e+18, 1.615146503312570855e+19, 3.242548467260718193e+19, 6.581494581080701321e+19, 1.350831366183090003e+20, 2.804093832520937396e+20, 5.888113683467563837e+20, 1.250923435312468276e+21, 2.689280279098215635e+21, 5.851582825664479700e+21, 1.288917231788944660e+22, 2.874582763768997631e+22, 6.492437335109217869e+22, 1.485286605867082177e+23, 3.442469159113307066e+23, 8.084930196860438207e+23, 1.924506778048094878e+24, 4.643992662491470729e+24, 1.136281452083591334e+25, 2.819664891060694571e+25, 7.097781559991856367e+25, 1.812838850127688486e+26, 4.699012851344539124e+26, 1.236419707162832951e+27, 3.303236261210411286e+27, 8.962558097638891218e+27, 2.470294852986226117e+28, 6.918270960555942883e+28, 1.969189447958411510e+29, 5.698092609453981289e+29, 1.676626156396922084e+30, 5.017901520171556970e+30, 1.527929892279834489e+31, 4.734762318366711949e+31, 1.493572546446777040e+32, 4.797441164681908184e+32, 1.569538296400998732e+33, 5.231651156910242454e+33, 1.777206511525290941e+34, 6.154587299576916134e+34, 2.173469781356604872e+35, 7.829529896526581616e+35, 2.877935554073076917e+36, 1.079761320923458592e+37, 4.136337730951207042e+37, 1.618408489711185844e+38, 6.469770640447824771e+38, 2.643413654859316358e+39, 1.104246728308525703e+40, 4.717842641881260665e+40, 2.062296462389327711e+41, 9.226680005161257219e+41, 4.226544071632731963e+42, 1.983043729707066518e+43, 9.533448690970155039e+43, 4.697914578740208606e+44, 2.373923101980436574e+45, 1.230570211868531753e+46, 6.546344338411695147e+46, 3.575371819335804914e+47, 2.005642453538335506e+48, 1.156055268028903078e+49, 6.849867807870312958e+49, 4.174004815218951121e+50, 2.616872034052857472e+51, 1.688750346837297725e+52, 1.122275666009684101e+53, 7.683968740248677071e+53, 5.422849612654278583e+54, 3.946686701799533415e+55, 2.963543587288132884e+56, 2.297086395798939516e+57, 1.838856414208555761e+58, 1.521049475711243996e+59, 1.300732291175071112e+60, 1.150559591141716740e+61, 1.053265997373725461e+62, 9.984114209879020836e+62, 9.805325615938694719e+63, 9.982463564199115995e+64, 1.054102211457911410e+66, 1.155172684780782463e+67, 1.314571302334116663e+68, 1.554362407685457310e+69, 1.910791206002645077e+70, 2.443616403890711206e+71, 3.252983822318823232e+72, 4.510600140020139737e+73, 6.518821831001902447e+74, 9.825834460774267633e+75, 1.545692063622722856e+77, 2.539346088408163253e+78, 4.359763993811836117e+79, 7.827943627464404744e+80, 1.470896877674301183e+82, 2.894527071420674290e+83, 5.969662541607915492e+84, 1.291277613981057357e+86, 2.931656535626877923e+87, 6.991353547531463135e+88, 1.752671194525972852e+90, 4.622450137056020715e+91, 1.283581933169566226e+93, 3.755839001138390788e+94, 1.158991729845978702e+96, 3.774916315438862678e+97, 1.298844894462381673e+99, 4.725038949943384889e+100, 1.819000031203286740e+102, 7.416966330876906188e+103, 3.206116996910598204e+105, 1.470588770071975193e+107, 7.164198238238641057e+108, 3.710397624567077270e+110, 2.044882454279709373e+112, 1.200428778654730225e+114, 7.513744370030172114e+115, 5.019575746343410636e+117, 3.582726927665698318e+119, 2.734947775877248560e+121, 2.235283764078944248e+123, 1.958084751118243323e+125, 1.840431913109305657e+127, 1.858143260692831108e+129, 2.017432949655777136e+131, 2.358177615888101494e+133, 2.971092974178603610e+135, 4.039532321435816302e+137, 5.933923069661132195e+139, 9.429263693444953240e+141, 1.622841456932873872e+144, 3.028884476067694180e+146, 6.138356175015339477e+148, 1.352531557191942648e+151, 3.244447362295582945e+153],
];

const EXP_SINH_WEIGHTS = [
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];

/**
 * Computes x * 2 ^ exp
 * Sourced from: http://croquetweak.blogspot.com/2014/08/deconstructing-floats-frexp-and-ldexp.html
 *
 * @param x mantissa
 * @param exp exponent
 * @return {*}
 */
function ldexp(x, exp) {
  let steps = Math.min(3, Math.ceil(Math.abs(exp) / 1023));
  let result = x;
  for (let i = 0; i < steps; i++) {
    result *= Math.pow(2, Math.floor((exp + i) / steps));
  }

  return result;
}

/**
 * Performs double exponential quadrature using the change of variable x = exp(pi/2 * sinh(t)), from Takahashi 1974.
 * The native range of this integrator is [0, inf].
 */
class ExpSinh {
  constructor(max_refinements = 9, tol = ROOT_EPSILON) {
    this.tol = tol;
    this.m_max_refinements = max_refinements;
    this.m_committed_refinements = EXP_SINH_WEIGHTS.length;
    this.m_t_min = -6.164062500000000000;
    this.m_abscissas = [...EXP_SINH_ABSCISSAS];
    this.m_weights = [...EXP_SINH_WEIGHTS];
  }

  extend_refinements() {
    if (this.m_committed_refinements >= this.m_max_refinements) {
      return;
    }

    let row = ++this.m_committed_refinements;
    let h = ldexp(1, -row);
    const t_max = this.m_t_min + this.m_abscissas[0].length - 1;
    let k = Math.trunc(Math.ceil((t_max - this.m_t_min) / (2 * h)));
    this.m_abscissas[row] = new Array(k);
    this.m_weights[row] = new Array(k);
    let arg = this.m_t_min;
    let j = 0;
    let l = 2;
    while (arg + l * h < t_max) {
      arg = this.m_t_min + (2 * j + 1) * h;
      let x = Math.exp(0.5 * Math.PI * Math.sinh(arg));
      this.m_abscissas[row].push(x);
      let w = Math.cosh(arg) * 0.5 * Math.PI * x;
      this.m_weights[row].push(w);
      ++j;
    }
  }

  get_abscissa_row(n) {
    if (this.m_committed_refinements < n) {
      this.extend_refinements();
    }

    return this.m_abscissas[n];
  }

  get_weight_row(n) {
    if (this.m_committed_refinements < n) {
      this.extend_refinements();
    }

    return this.m_weights[n];
  }

  integrate(f, a, b) {
    let integrand = f;
    if (isFinite(a) && (b >= Number.MAX_VALUE)) {
      if (a !== 0) {
        integrand = (x) => f(x + a);
      }
    }

    if (isFinite(b) && (a <= -Number.MAX_VALUE)) {
      integrand = (x) => f(b - x);
    }

    if (a <= -Number.MAX_VALUE && b >= Number.MAX_VALUE) {
      throw new RangeError('Error: use sinh_sinh quadrature for integration over entire real line, exp_sinh is for half infinite [0, inf]');
    }

    let y_max = integrand(Number.MAX_VALUE);
    if (Math.abs(y_max) > Number.EPSILON || !isFinite(y_max)) {
      throw new RangeError('Error: integrated function does not go to zero at infinity');
    }

    let I0 = 0;
    let L1_I0 = 0;
    for (let i = 0; i < this.m_abscissas[0].length; i++) {
      let y = integrand(this.m_abscissas[0][i]);
      I0 += y * this.m_weights[0][i];
      L1_I0 += Math.abs(y) * this.m_weights[0][i];
    }

    let I1 = I0;
    let L1_I1 = L1_I0;
    for (let i = 0; i < this.m_abscissas[1].length; i++) {
      let y = integrand(this.m_abscissas[1][i]);
      I1 += y * this.m_weights[1][i];
      L1_I1 += Math.abs(y) * this.m_weights[1][i];
    }

    I1 *= 0.5;
    L1_I1 *= 0.5;
    let err = Math.abs(I0 - I1);
    let i = 2;
    for (; i < this.m_abscissas.length; i++) {
      I0 = I1;
      L1_I0 = L1_I1;

      I1 = 0.5 * I0;
      L1_I1 = 0.5 * L1_I0;
      let h = 1 / (1 << i);
      let sum = 0;
      let absum = 0;

      let abscissas_row = this.get_abscissa_row(i);
      let weight_row = this.get_weight_row(i);

      let abterm1 = 1;
      let eps = Number.EPSILON * L1_I1;
      for (let j = 0; j < this.m_weights[i].length; j++) {
        let x = abscissas_row[j];
        let y = integrand(x);
        sum += y * weight_row[j];
        let abterm0 = Math.abs(y) * weight_row[j];
        absum += abterm0;

        if (x > 100 && abterm0 < eps && abterm1 < eps) {
          break;
        }

        abterm1 = abterm0;
      }

      I1 += sum * h;
      L1_I1 += absum * h;
      err = Math.abs(I0 - I1);
      if (!isFinite(I1)) {
        throw new RangeError('Error: function was evaluated at singular point - ensure function is finite over entire domain');
      }

      if (err <= this.tol * L1_I1) {
        break;
      }
    }

    return [I1, err];
  }
}

export { GaussKronrod, ExpSinh };