#include <math.h>

#define grNTAU          102
#define grNK          200
const double grTAUarr[         102]={
      -6.9077553,
      -4.6051702,
      -4.4888780,
      -4.3725858,
      -4.2562937,
      -4.1400015,
      -4.0237093,
      -3.9074171,
      -3.7911250,
      -3.6748328,
      -3.5585406,
      -3.4422484,
      -3.3259562,
      -3.2096641,
      -3.0933719,
      -2.9770797,
      -2.8607875,
      -2.7444954,
      -2.6282032,
      -2.5119110,
      -2.3956188,
      -2.2793267,
      -2.1630345,
      -2.0467423,
      -1.9304501,
      -1.8141580,
      -1.6978658,
      -1.5815736,
      -1.4652814,
      -1.3489892,
      -1.2326971,
      -1.1164049,
      -1.0001127,
     -0.88382054,
     -0.76752836,
     -0.65123619,
     -0.53494401,
     -0.41865184,
     -0.30235966,
     -0.18606748,
    -0.069775306,
     0.046516871,
      0.16280905,
      0.27910122,
      0.39539340,
      0.51168558,
      0.62797775,
      0.74426993,
      0.86056211,
      0.97685428,
       1.0931465,
       1.2094386,
       1.3257308,
       1.4420230,
       1.5583152,
       1.6746073,
       1.7908995,
       1.9071917,
       2.0234839,
       2.1397760,
       2.2560682,
       2.3723604,
       2.4886526,
       2.6049448,
       2.7212369,
       2.8375291,
       2.9538213,
       3.0701135,
       3.1864056,
       3.3026978,
       3.4189900,
       3.5352822,
       3.6515743,
       3.7678665,
       3.8841587,
       4.0004509,
       4.1167430,
       4.2330352,
       4.3493274,
       4.4656196,
       4.5819118,
       4.6982039,
       4.8144961,
       4.9307883,
       5.0470805,
       5.1633726,
       5.2796648,
       5.3959570,
       5.5122492,
       5.6285413,
       5.7448335,
       5.8611257,
       5.9774179,
       6.0937100,
       6.2100022,
       6.3262944,
       6.4425866,
       6.5588787,
       6.6751709,
       6.7914631,
       6.9077553,
       9.2103404};
const double grKarr[         200]={
     -0.51082562,
     -0.48511710,
     -0.45940858,
     -0.43370006,
     -0.40799154,
     -0.38228302,
     -0.35657449,
     -0.33086597,
     -0.30515745,
     -0.27944893,
     -0.25374041,
     -0.22803189,
     -0.20232336,
     -0.17661484,
     -0.15090632,
     -0.12519780,
    -0.099489277,
    -0.073780756,
    -0.048072234,
    -0.022363712,
    0.0033448094,
     0.029053331,
     0.054761853,
     0.080470374,
      0.10617890,
      0.13188742,
      0.15759594,
      0.18330446,
      0.20901298,
      0.23472150,
      0.26043003,
      0.28613855,
      0.31184707,
      0.33755559,
      0.36326411,
      0.38897263,
      0.41468116,
      0.44038968,
      0.46609820,
      0.49180672,
      0.51751524,
      0.54322376,
      0.56893229,
      0.59464081,
      0.62034933,
      0.64605785,
      0.67176637,
      0.69747489,
      0.72318342,
      0.74889194,
      0.77460046,
      0.80030898,
      0.82601750,
      0.85172602,
      0.87743455,
      0.90314307,
      0.92885159,
      0.95456011,
      0.98026863,
       1.0059772,
       1.0316857,
       1.0573942,
       1.0831027,
       1.1088112,
       1.1345198,
       1.1602283,
       1.1859368,
       1.2116453,
       1.2373538,
       1.2630624,
       1.2887709,
       1.3144794,
       1.3401879,
       1.3658965,
       1.3916050,
       1.4173135,
       1.4430220,
       1.4687305,
       1.4944391,
       1.5201476,
       1.5458561,
       1.5715646,
       1.5972732,
       1.6229817,
       1.6486902,
       1.6743987,
       1.7001072,
       1.7258158,
       1.7515243,
       1.7772328,
       1.8029413,
       1.8286498,
       1.8543584,
       1.8800669,
       1.9057754,
       1.9314839,
       1.9571925,
       1.9829010,
       2.0086095,
       2.0343180,
       2.0600265,
       2.0857351,
       2.1114436,
       2.1371521,
       2.1628606,
       2.1885692,
       2.2142777,
       2.2399862,
       2.2656947,
       2.2914032,
       2.3171118,
       2.3428203,
       2.3685288,
       2.3942373,
       2.4199458,
       2.4456544,
       2.4713629,
       2.4970714,
       2.5227799,
       2.5484885,
       2.5741970,
       2.5999055,
       2.6256140,
       2.6513225,
       2.6770311,
       2.7027396,
       2.7284481,
       2.7541566,
       2.7798651,
       2.8055737,
       2.8312822,
       2.8569907,
       2.8826992,
       2.9084078,
       2.9341163,
       2.9598248,
       2.9855333,
       3.0112418,
       3.0369504,
       3.0626589,
       3.0883674,
       3.1140759,
       3.1397845,
       3.1654930,
       3.1912015,
       3.2169100,
       3.2426185,
       3.2683271,
       3.2940356,
       3.3197441,
       3.3454526,
       3.3711611,
       3.3968697,
       3.4225782,
       3.4482867,
       3.4739952,
       3.4997038,
       3.5254123,
       3.5511208,
       3.5768293,
       3.6025378,
       3.6282464,
       3.6539549,
       3.6796634,
       3.7053719,
       3.7310804,
       3.7567890,
       3.7824975,
       3.8082060,
       3.8339145,
       3.8596231,
       3.8853316,
       3.9110401,
       3.9367486,
       3.9624571,
       3.9881657,
       4.0138742,
       4.0395827,
       4.0652912,
       4.0909998,
       4.1167083,
       4.1424168,
       4.1681253,
       4.1938338,
       4.2195424,
       4.2452509,
       4.2709594,
       4.2966679,
       4.3223764,
       4.3480850,
       4.3737935,
       4.3995020,
       4.4252105,
       4.4509191,
       4.4766276,
       4.5023361,
       4.5280446,
       4.5537531,
       4.5794617,
       4.6051702};
const double grR[         102][         200]={
    -0.083739330,
    -0.055827023,
    -0.037026458,
    -0.024389538,
    -0.015936217,
    -0.010319362,
   -0.0066174230,
   -0.0041998596,
   -0.0026367653,
   -0.0016368403,
   -0.0010042997,
  -0.00060880257,
  -0.00036448901,
  -0.00021544005,
  -0.00012567191,
 -7.2318151e-005,
 -4.1036092e-005,
 -2.2949819e-005,
 -1.2642202e-005,
 -6.8539299e-006,
 -3.6525474e-006,
 -1.9094322e-006,
 -9.7555166e-007,
 -4.8355222e-007,
 -2.2887470e-007,
 -9.9502341e-008,
 -3.5140064e-008,
 -3.9004544e-009,
  1.0777228e-008,
  1.7335508e-008,
  1.9996531e-008,
  2.0830659e-008,
  2.0832652e-008,
  2.0470374e-008,
  1.9959070e-008,
  1.9395376e-008,
  1.8821404e-008,
  1.8254885e-008,
  1.7702771e-008,
  1.7167553e-008,
  1.6649715e-008,
  1.6149145e-008,
  1.5665259e-008,
  1.5197581e-008,
  1.4745389e-008,
  1.4308254e-008,
  1.3885458e-008,
  1.3476559e-008,
  1.3081013e-008,
  1.2698344e-008,
  1.2327995e-008,
  1.1969599e-008,
  1.1622687e-008,
  1.1286880e-008,
  1.0961681e-008,
  1.0646796e-008,
  1.0341837e-008,
  1.0046394e-008,
  9.7601775e-009,
  9.4829124e-009,
  9.2141836e-009,
  8.9537524e-009,
  8.7013030e-009,
  8.4565927e-009,
  8.2193336e-009,
  7.9892543e-009,
  7.7661257e-009,
  7.5497459e-009,
  7.3398234e-009,
  7.1362374e-009,
  6.9386494e-009,
  6.7469343e-009,
  6.5609449e-009,
  6.3804593e-009,
  6.2052281e-009,
  6.0351468e-009,
  5.8700118e-009,
  5.7096949e-009,
  5.5540434e-009,
  5.4029068e-009,
  5.2561064e-009,
  5.1135362e-009,
  4.9750266e-009,
  4.8405295e-009,
  4.7098512e-009,
  4.5829207e-009,
  4.4595496e-009,
  4.3397112e-009,
  4.2232311e-009,
  4.1100085e-009,
  4.0000105e-009,
  3.8930898e-009,
  3.7891543e-009,
  3.6880761e-009,
  3.5898855e-009,
  3.4944076e-009,
  3.4015490e-009,
  3.3112864e-009,
  3.2234955e-009,
  3.1381591e-009,
  3.0551586e-009,
  2.9744125e-009,
  2.8959037e-009,
  2.8194949e-009,
  2.7452449e-009,
  2.6729880e-009,
  2.6026781e-009,
  2.5343121e-009,
  2.4677687e-009,
  2.4030515e-009,
  2.3401165e-009,
  2.2788458e-009,
  2.2192115e-009,
  2.1612185e-009,
  2.1047548e-009,
  2.0498061e-009,
  1.9963808e-009,
  1.9443627e-009,
  1.8936996e-009,
  1.8444326e-009,
  1.7964827e-009,
  1.7498230e-009,
  1.7043851e-009,
  1.6601671e-009,
  1.6170616e-009,
  1.5751587e-009,
  1.5343486e-009,
  1.4946357e-009,
  1.4559702e-009,
  1.4183026e-009,
  1.3816253e-009,
  1.3459651e-009,
  1.3111963e-009,
  1.2773573e-009,
  1.2443970e-009,
  1.2123134e-009,
  1.1810366e-009,
  1.1506192e-009,
  1.1209904e-009,
  1.0921499e-009,
  1.0640167e-009,
  1.0366579e-009,
  1.0100345e-009,
  9.8404351e-010,
  9.5876107e-010,
  9.3414787e-010,
  9.1014929e-010,
  8.8679508e-010,
  8.6403462e-010,
  8.4188056e-010,
  8.2027007e-010,
  7.9924689e-010,
  7.7879969e-010,
  7.5879925e-010,
  7.3935169e-010,
  7.2044637e-010,
  7.0193917e-010,
  6.8397510e-010,
  6.6650352e-010,
  6.4943340e-010,
  6.3282624e-010,
  6.1661209e-010,
  6.0085648e-010,
  5.8550609e-010,
  5.7052585e-010,
  5.5596860e-010,
  5.4172977e-010,
  5.2791105e-010,
  5.1442206e-010,
  5.0128723e-010,
  4.8846949e-010,
  4.7595283e-010,
  4.6383364e-010,
  4.5201887e-010,
  4.4047188e-010,
  4.2924264e-010,
  4.1825965e-010,
  4.0760262e-010,
  3.9715453e-010,
  3.8709747e-010,
  3.7719472e-010,
  3.6759329e-010,
  3.5823344e-010,
  3.4905745e-010,
  3.4013659e-010,
  3.3145908e-010,
  3.2304737e-010,
  3.1477665e-010,
  3.0670932e-010,
  2.9900948e-010,
  2.9123948e-010,
  2.8388469e-010,
  2.7660096e-010,
  2.6960789e-010,
  2.6271718e-010,
  2.5604541e-010,
  2.4945201e-010,
  2.4313485e-010,
  2.3694913e-010,
  2.3082447e-010,
    -0.083733191,
    -0.055821068,
    -0.037020689,
    -0.024383953,
    -0.015930815,
    -0.010314139,
   -0.0066123764,
   -0.0041949843,
   -0.0026320564,
   -0.0016322924,
  -0.00099990730,
  -0.00060456022,
  -0.00036039124,
  -0.00021148148,
  -0.00012184731,
 -6.8622446e-005,
 -3.7464384e-005,
 -1.9497396e-005,
 -9.3045367e-006,
 -3.6266799e-006,
 -5.3154940e-007,
  1.1093024e-006,
  1.9447399e-006,
  2.3419557e-006,
  2.5053547e-006,
  2.5468064e-006,
  2.5264651e-006,
  2.4760838e-006,
  2.4120952e-006,
  2.3428197e-006,
  2.2723626e-006,
  2.2026831e-006,
  2.1346697e-006,
  2.0686891e-006,
  2.0048598e-006,
  1.9431858e-006,
  1.8836214e-006,
  1.8260999e-006,
  1.7705479e-006,
  1.7168910e-006,
  1.6650563e-006,
  1.6149733e-006,
  1.5665746e-006,
  1.5197954e-006,
  1.4745738e-006,
  1.4308504e-006,
  1.3885686e-006,
  1.3476741e-006,
  1.3081149e-006,
  1.2698414e-006,
  1.2328060e-006,
  1.1969629e-006,
  1.1622687e-006,
  1.1286813e-006,
  1.0961607e-006,
  1.0646685e-006,
  1.0341678e-006,
  1.0046232e-006,
  9.7600086e-007,
  9.4826821e-007,
  9.2139407e-007,
  8.9534848e-007,
  8.7010268e-007,
  8.4562898e-007,
  8.2190097e-007,
  7.9889309e-007,
  7.7658085e-007,
  7.5494073e-007,
  7.3395014e-007,
  7.1358726e-007,
  6.9383122e-007,
  6.7466192e-007,
  6.5605990e-007,
  6.3800659e-007,
  6.2048405e-007,
  6.0347506e-007,
  5.8696288e-007,
  5.7093157e-007,
  5.5536569e-007,
  5.4025035e-007,
  5.2557124e-007,
  5.1131456e-007,
  4.9746695e-007,
  4.8401562e-007,
  4.7094818e-007,
  4.5825262e-007,
  4.4591746e-007,
  4.3393160e-007,
  4.2228420e-007,
  4.1096501e-007,
  3.9996391e-007,
  3.8927129e-007,
  3.7887781e-007,
  3.6877441e-007,
  3.5895238e-007,
  3.4940328e-007,
  3.4011905e-007,
  3.3109167e-007,
  3.2231364e-007,
  3.1377749e-007,
  3.0547620e-007,
  2.9740282e-007,
  2.8955069e-007,
  2.8191336e-007,
  2.7448450e-007,
  2.6725821e-007,
  2.6022852e-007,
  2.5338981e-007,
  2.4673657e-007,
  2.4026349e-007,
  2.3396546e-007,
  2.2783742e-007,
  2.2187462e-007,
  2.1607224e-007,
  2.1042586e-007,
  2.0493104e-007,
  1.9958348e-007,
  1.9437908e-007,
  1.8931382e-007,
  1.8438380e-007,
  1.7958524e-007,
  1.7491458e-007,
  1.7036810e-007,
  1.6594248e-007,
  1.6163428e-007,
  1.5744035e-007,
  1.5335749e-007,
  1.4938266e-007,
  1.4551288e-007,
  1.4174528e-007,
  1.3807710e-007,
  1.3450557e-007,
  1.3102806e-007,
  1.2764205e-007,
  1.2434505e-007,
  1.2113460e-007,
  1.1800840e-007,
  1.1496418e-007,
  1.1199967e-007,
  1.0911278e-007,
  1.0630136e-007,
  1.0356345e-007,
  1.0089708e-007,
  9.8300201e-008,
  9.5771108e-008,
  9.3307951e-008,
  9.0908902e-008,
  8.8572331e-008,
  8.6296498e-008,
  8.4079874e-008,
  8.1920813e-008,
  7.9817812e-008,
  7.7769404e-008,
  7.5774093e-008,
  7.3830541e-008,
  7.1937333e-008,
  7.0093109e-008,
  6.8296686e-008,
  6.6546704e-008,
  6.4841930e-008,
  6.3181292e-008,
  6.1563476e-008,
  5.9987459e-008,
  5.8452194e-008,
  5.6956428e-008,
  5.5499325e-008,
  5.4079699e-008,
  5.2696725e-008,
  5.1349372e-008,
  5.0036694e-008,
  4.8757814e-008,
  4.7511791e-008,
  4.6297919e-008,
  4.5115199e-008,
  4.3962876e-008,
  4.2840190e-008,
  4.1746304e-008,
  4.0680558e-008,
  3.9642088e-008,
  3.8630403e-008,
  3.7644581e-008,
  3.6684100e-008,
  3.5748224e-008,
  3.4836306e-008,
  3.3947780e-008,
  3.3082037e-008,
  3.2238493e-008,
  3.1416511e-008,
  3.0615613e-008,
  2.9835288e-008,
  2.9074736e-008,
  2.8333817e-008,
  2.7611775e-008,
  2.6908297e-008,
  2.6222722e-008,
  2.5554697e-008,
  2.4903723e-008,
  2.4269459e-008,
  2.3651364e-008,
  2.3048979e-008,
    -0.083731567,
    -0.055819493,
    -0.037019163,
    -0.024382476,
    -0.015929386,
    -0.010312758,
   -0.0066110416,
   -0.0041936948,
   -0.0026308109,
   -0.0016310894,
  -0.00099874551,
  -0.00060343812,
  -0.00035930737,
  -0.00021043443,
  -0.00012083570,
 -6.7644929e-005,
 -3.6519665e-005,
 -1.8584228e-005,
 -8.4217219e-006,
 -2.7730699e-006,
  2.9395696e-007,
  1.9077599e-006,
  2.7171593e-006,
  3.0893048e-006,
  3.2285607e-006,
  3.2467573e-006,
  3.2040118e-006,
  3.1320418e-006,
  3.0472460e-006,
  2.9579123e-006,
  2.8681154e-006,
  2.7797850e-006,
  2.6937815e-006,
  2.6104449e-006,
  2.5298678e-006,
  2.4520302e-006,
  2.3768627e-006,
  2.3042766e-006,
  2.2341771e-006,
  2.1664695e-006,
  2.1010614e-006,
  2.0378639e-006,
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extern "C" double RFactorKappaApprox(double tau, double k)
{
 double logtau=log(tau);
 double logk=log(k);

 if (logk>grKarr[grNK-1]) return 1.0;
 else
 {
  int j1, j2, k1, k2, l;

  if (logtau<=grTAUarr[0])
  {
   j1=0;
   j2=1;
  }
  else if (logtau>=grTAUarr[grNTAU-1])
  {
   j1=grNTAU-2;
   j2=grNTAU-1;
  }
  else
  {
   j1=0;
   j2=grNTAU-1;
   while ((j2-j1)>1)
   {
    l=(j2+j1)>>1;
    if (grTAUarr[l]>logtau) j2=l;
    else j1=l;
   }
  }
  double dx=grTAUarr[j2]-grTAUarr[j1];
  double t=(logtau-grTAUarr[j1])/dx;

  if (logk<=grKarr[0])
  {
   k1=0;
   k2=1;
  }
  else if (logk>=grKarr[grNK-1])
  {
   k1=grNK-2;
   k2=grNK-1;
  }
  else
  {
   k1=0;
   k2=grNK-1;
   while ((k2-k1)>1)
   {
    l=(k2+k1)>>1;
    if (grKarr[l]>logk) k2=l;
    else k1=l;
   }
  }
  double dy=grKarr[k2]-grKarr[k1];
  double u=(logk-grKarr[k1])/dy;

  double f1=grR[j1][k1];
  double f2=grR[j2][k1];
  double f3=grR[j2][k2];
  double f4=grR[j1][k2];

  return exp((1.0-t)*(1.0-u)*f1+t*(1.0-u)*f2+t*u*f3+(1.0-t)*u*f4);
 }
}