#include <math.h>
#include <float.h>
#include "ExtMath.h"

#define Ns           19
const int s_arr[Ns]={
       2,
       3,
       4,
       5,
       6,
       7,
       8,
       9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19,
      20};
#define Nk            8
const int k_arr[Nk]={
       0,
       1,
       2,
       3,
       4,
       5,
       6,
       7};
#define Ntau1          100
const double logtau1_arr[Ntau1]={
      -6.9077553,
      -6.7449462,
      -6.5821372,
      -6.4193281,
      -6.2565191,
      -6.0937100,
      -5.9309010,
      -5.7680920,
      -5.6052829,
      -5.4424739,
      -5.2796648,
      -5.1168558,
      -4.9540467,
      -4.7912377,
      -4.6284286,
      -4.4656196,
      -4.3028105,
      -4.1400015,
      -3.9771924,
      -3.8143834,
      -3.6515743,
      -3.4887653,
      -3.3259562,
      -3.1631472,
      -3.0003382,
      -2.8375291,
      -2.6747201,
      -2.5119110,
      -2.3491020,
      -2.1862929,
      -2.0234839,
      -1.8606748,
      -1.6978658,
      -1.5350567,
      -1.3722477,
      -1.2094386,
      -1.0466296,
     -0.88382054,
     -0.72101149,
     -0.55820245,
     -0.39539340,
     -0.23258435,
    -0.069775306,
     0.093033741,
      0.25584279,
      0.41865184,
      0.58146088,
      0.74426993,
      0.90707898,
       1.0698880,
       1.2326971,
       1.3955061,
       1.5583152,
       1.7211242,
       1.8839333,
       2.0467423,
       2.2095514,
       2.3723604,
       2.5351694,
       2.6979785,
       2.8607875,
       3.0235966,
       3.1864056,
       3.3492147,
       3.5120237,
       3.6748328,
       3.8376418,
       4.0004509,
       4.1632599,
       4.3260690,
       4.4888780,
       4.6516871,
       4.8144961,
       4.9773052,
       5.1401142,
       5.3029232,
       5.4657323,
       5.6285413,
       5.7913504,
       5.9541594,
       6.1169685,
       6.2797775,
       6.4425866,
       6.6053956,
       6.7682047,
       6.9310137,
       7.0938228,
       7.2566318,
       7.4194409,
       7.5822499,
       7.7450589,
       7.9078680,
       8.0706770,
       8.2334861,
       8.3962951,
       8.5591042,
       8.7219132,
       8.8847223,
       9.0475313,
       9.2103404};
const double logR1_arr[Ns][Nk][Ntau1]={
  1.8518520e-013,
  1.2656542e-013,
  1.1124435e-013,
  1.6076029e-013,
  1.5210055e-013,
  1.6764368e-013,
  1.5476509e-013,
  1.3611334e-013,
  1.3100632e-013,
  1.5853985e-013,
  1.7674751e-013,
  1.5432100e-013,
  1.5809576e-013,
  1.5365487e-013,
  1.4543922e-013,
  1.4788171e-013,
  1.4432899e-013,
  1.3744561e-013,
  1.3145041e-013,
  1.3788970e-013,
  1.4366286e-013,
  1.5498713e-013,
  1.5676349e-013,
  1.2723156e-013,
  1.5476509e-013,
  1.4876989e-013,
  1.5276669e-013,
  1.3056223e-013,
  1.2811974e-013,
  1.3145041e-013,
  1.2145840e-013,
  1.3633539e-013,
  1.1257661e-013,
  1.2412293e-013,
  1.2589929e-013,
  1.2989609e-013,
  1.2212453e-013,
  1.4055423e-013,
  1.1723955e-013,
  9.3480779e-014,
  1.0502710e-013,
  8.6375351e-014,
  9.5923269e-014,
  4.3298698e-014,
  5.2402527e-014,
  6.6613381e-014,
  2.5979219e-014,
  3.6415315e-014,
  1.0658141e-014,
  2.7977620e-014,
  1.8873791e-014,
 -1.3322676e-015,
 -3.7747583e-015,
 -1.8318680e-014,
 -6.9944051e-015,
 -1.6320278e-014,
 -2.5757174e-014,
 -2.3536728e-014,
 -3.3528735e-014,
 -2.1649349e-014,
 -3.3861802e-014,
 -5.6843419e-014,
 -1.3300472e-013,
 -2.8610447e-013,
 -3.0742076e-013,
 -2.8033131e-013,
 -2.7633451e-013,
 -2.7611247e-013,
 -1.3800072e-013,
 -1.3788970e-013,
 -1.3788970e-013,
 -1.3788970e-013,
 -6.9055872e-014,
 -6.9055872e-014,
 -6.9055872e-014,
 -6.9055872e-014,
 -3.4527936e-014,
 -3.4527936e-014,
 -3.4527936e-014,
 -3.4527936e-014,
 -3.4527936e-014,
 -1.7208457e-014,
 -1.7208457e-014,
 -1.7208457e-014,
 -1.6986412e-014,
 -8.5487173e-015,
 -8.5487173e-015,
 -8.7707619e-015,
 -8.5487173e-015,
 -4.3298698e-015,
 -4.3298698e-015,
 -4.3298698e-015,
 -4.3298698e-015,
 -1.9984014e-015,
 -1.9984014e-015,
 -2.2204460e-015,
 -1.9984014e-015,
 -2.1094237e-015,
 -8.8817842e-016,
 -8.8817842e-016,
 -2.4503727e-009,
 -3.3935063e-009,
 -4.6996297e-009,
 -6.5083739e-009,
 -9.0133579e-009,
 -1.2482470e-008,
 -1.7286774e-008,
 -2.3940218e-008,
 -3.3154482e-008,
 -4.5915129e-008,
 -6.3587198e-008,
 -8.8061007e-008,
 -1.2195445e-007,
 -1.6889297e-007,
 -2.3389738e-007,
 -3.2392101e-007,
 -4.4859330e-007,
 -6.2124974e-007,
 -8.6035841e-007,
 -1.1914951e-006,
 -1.6500784e-006,
 -2.2851578e-006,
 -3.1646587e-006,
 -4.3826442e-006,
 -6.0693714e-006,
 -8.4052115e-006,
 -1.1639921e-005,
 -1.6119313e-005,
 -2.2322160e-005,
 -3.0911245e-005,
 -4.2803940e-005,
 -5.9269732e-005,
 -8.2064856e-005,
  -0.00011361794,
  -0.00015728552,
  -0.00021770300,
  -0.00030126491,
  -0.00041677929,
  -0.00057635345,
  -0.00079658181,
   -0.0011001181,
   -0.0015177164,
   -0.0020908069,
   -0.0028746050,
   -0.0039416023,
   -0.0053849910,
   -0.0073210679,
   -0.0098889189,
    -0.013244827,
    -0.017548321,
    -0.022937573,
    -0.029495227,
    -0.037212167,
    -0.045963654,
    -0.055513623,
    -0.065552884,
    -0.075758782,
    -0.085851237,
    -0.095624455,
     -0.10495051,
     -0.11376513,
     -0.12204838,
     -0.12980797,
     -0.13706719,
     -0.14385706,
     -0.15021150,
     -0.15616456,
     -0.16174887,
     -0.16699495,
     -0.17193087,
     -0.17658221,
     -0.18097221,
     -0.18512187,
     -0.18905015,
     -0.19277421,
     -0.19630953,
     -0.19967013,
     -0.20286869,
     -0.20591675,
     -0.20882475,
     -0.21160224,
     -0.21425790,
     -0.21679967,
     -0.21923481,
     -0.22156999,
     -0.22381131,
     -0.22596440,
     -0.22803445,
     -0.23002623,
     -0.23194418,
     -0.23379237,
     -0.23557461,
     -0.23729442,
     -0.23895506,
     -0.24055959,
     -0.24211084,
     -0.24361147,
     -0.24506394,
     -0.24647058,
     -0.24783355,
 -3.9059174e-009,
 -5.4092081e-009,
 -7.4910307e-009,
 -1.0374091e-008,
 -1.4366810e-008,
 -1.9896302e-008,
 -2.7554005e-008,
 -3.8159086e-008,
 -5.2845906e-008,
 -7.3185437e-008,
 -1.0135337e-007,
 -1.4036278e-007,
 -1.9438636e-007,
 -2.6920280e-007,
 -3.7281497e-007,
 -5.1630586e-007,
 -7.1502406e-007,
 -9.9022550e-007,
 -1.3713468e-006,
 -1.8991539e-006,
 -2.6301017e-006,
 -3.6423717e-006,
 -5.0442320e-006,
 -6.9856137e-006,
 -9.6741383e-006,
 -1.3397308e-005,
 -1.8553225e-005,
 -2.5693101e-005,
 -3.5580095e-005,
 -4.9270686e-005,
 -6.8227202e-005,
 -9.4473309e-005,
  -0.00013080870,
  -0.00018110516,
  -0.00025071418,
  -0.00034702694,
  -0.00048024103,
  -0.00066440569,
  -0.00091883792,
   -0.0012700239,
   -0.0017541398,
   -0.0024203341,
   -0.0033348842,
   -0.0045862478,
   -0.0062907965,
   -0.0085985672,
    -0.011697580,
    -0.015814100,
    -0.021204812,
    -0.028135937,
    -0.036845289,
    -0.047488259,
    -0.060078619,
    -0.074446415,
    -0.090238567,
     -0.10697349,
     -0.12413271,
     -0.14125082,
     -0.15797009,
     -0.17405152,
     -0.18935732,
     -0.20382408,
     -0.21743852,
     -0.23021905,
     -0.24220289,
     -0.25343715,
     -0.26397314,
     -0.27386270,
     -0.28315604,
     -0.29190053,
     -0.30014018,
     -0.30791540,
     -0.31526313,
     -0.32221694,
     -0.32880730,
     -0.33506185,
     -0.34100565,
     -0.34666141,
     -0.35204979,
     -0.35718952,
     -0.36209770,
     -0.36678989,
     -0.37128029,
     -0.37558192,
     -0.37970668,
     -0.38366550,
     -0.38746842,
     -0.39112468,
     -0.39464282,
     -0.39803070,
     -0.40129561,
     -0.40444428,
     -0.40748296,
     -0.41041748,
     -0.41325322,
     -0.41599522,
     -0.41864817,
     -0.42121644,
     -0.42370414,
     -0.42611508,
 -4.8727960e-009,
 -6.7481218e-009,
 -9.3451902e-009,
 -1.2941731e-008,
 -1.7922642e-008,
 -2.4820625e-008,
 -3.4373528e-008,
 -4.7603256e-008,
 -6.5924893e-008,
 -9.1298277e-008,
 -1.2643747e-007,
 -1.7510133e-007,
 -2.4249516e-007,
 -3.3582789e-007,
 -4.6508301e-007,
 -6.4408640e-007,
 -8.9198532e-007,
 -1.2352963e-006,
 -1.7107413e-006,
 -2.3691754e-006,
 -3.2810257e-006,
 -4.5438230e-006,
 -6.2926312e-006,
 -8.7144885e-006,
 -1.2068403e-005,
 -1.6713033e-005,
 -2.3145014e-005,
 -3.2051990e-005,
 -4.4386017e-005,
 -6.1465088e-005,
 -8.5113532e-005,
  -0.00011785602,
  -0.00016318547,
  -0.00022593251,
  -0.00031277429,
  -0.00043293351,
  -0.00059913593,
  -0.00082891625,
   -0.0011463882,
   -0.0015846234,
   -0.0021888092,
   -0.0030203665,
   -0.0041621809,
   -0.0057249842,
   -0.0078546530,
    -0.010739636,
    -0.014616765,
    -0.019772251,
    -0.026532901,
    -0.035241326,
    -0.046209875,
    -0.059653940,
    -0.075617274,
    -0.093916304,
     -0.11413556,
     -0.13568998,
     -0.15793511,
     -0.18027877,
     -0.20225150,
     -0.22352458,
     -0.24389251,
     -0.26324365,
     -0.28153285,
     -0.29876019,
     -0.31495522,
     -0.33016558,
     -0.34444878,
     -0.35786659,
     -0.37048134,
     -0.38235352,
     -0.39354051,
     -0.40409579,
     -0.41406878,
     -0.42350475,
     -0.43244506,
     -0.44092734,
     -0.44898584,
     -0.45665166,
     -0.46395310,
     -0.47091590,
     -0.47756349,
     -0.48391723,
     -0.48999663,
     -0.49581954,
     -0.50140226,
     -0.50675979,
     -0.51190586,
     -0.51685314,
     -0.52161329,
     -0.52619704,
     -0.53061436,
     -0.53487443,
     -0.53898578,
     -0.54295632,
     -0.54679341,
     -0.55050389,
     -0.55409414,
     -0.55757009,
     -0.56093732,
     -0.56420101,
 -5.5627649e-009,
 -7.7035219e-009,
 -1.0668199e-008,
 -1.4773848e-008,
 -2.0459801e-008,
 -2.8334183e-008,
 -3.9239312e-008,
 -5.4341688e-008,
 -7.5256739e-008,
 -1.0422168e-007,
 -1.4433484e-007,
 -1.9988702e-007,
 -2.7682039e-007,
 -3.8336431e-007,
 -5.3091541e-007,
 -7.3525664e-007,
 -1.0182455e-006,
 -1.4101520e-006,
 -1.9528961e-006,
 -2.7045313e-006,
 -3.7454539e-006,
 -5.1870002e-006,
 -7.1833527e-006,
 -9.9480257e-006,
 -1.3776691e-005,
 -1.9078778e-005,
 -2.6421225e-005,
 -3.6589023e-005,
 -5.0669011e-005,
 -7.0165781e-005,
 -9.7161968e-005,
  -0.00013453975,
  -0.00018628674,
  -0.00025791785,
  -0.00035705638,
  -0.00049423238,
  -0.00068397660,
  -0.00094631269,
   -0.0013087809,
   -0.0018091594,
   -0.0024990797,
   -0.0034487473,
   -0.0047529503,
   -0.0065384122,
   -0.0089722448,
    -0.012270639,
    -0.016705856,
    -0.022607936,
    -0.030355517,
    -0.040348635,
    -0.052957328,
    -0.068446264,
    -0.086889053,
     -0.10810232,
     -0.13163615,
     -0.15684010,
     -0.18298511,
     -0.20938954,
     -0.23550092,
     -0.26091932,
     -0.28538098,
     -0.30872823,
     -0.33088122,
     -0.35181573,
     -0.37154624,
     -0.39011307,
     -0.40757253,
     -0.42398981,
     -0.43943371,
     -0.45397320,
     -0.46767517,
     -0.48060304,
     -0.49281608,
     -0.50436914,
     -0.51531261,
     -0.52569261,
     -0.53555123,
     -0.54492683,
     -0.55385431,
     -0.56236550,
     -0.57048938,
     -0.57825239,
     -0.58567865,
     -0.59279024,
     -0.59960734,
     -0.60614847,
     -0.61243062,
     -0.61846942,
     -0.62427925,
     -0.62987337,
     -0.63526405,
     -0.64046260,
     -0.64547953,
     -0.65032456,
     -0.65500674,
     -0.65953448,
     -0.66391559,
     -0.66815739,
     -0.67226668,
     -0.67624983,
 -6.0803961e-009,
 -8.4202534e-009,
 -1.1660650e-008,
 -1.6148162e-008,
 -2.2362921e-008,
 -3.0969649e-008,
 -4.2889007e-008,
 -5.9395934e-008,
 -8.2256162e-008,
 -1.1391499e-007,
 -1.5775879e-007,
 -2.1847753e-007,
 -3.0256601e-007,
 -4.1901894e-007,
 -5.8029284e-007,
 -8.0363858e-007,
 -1.1129465e-006,
 -1.5413018e-006,
 -2.1345233e-006,
 -2.9560636e-006,
 -4.0937964e-006,
 -5.6694126e-006,
 -7.8514349e-006,
 -1.0873236e-005,
 -1.5057986e-005,
 -2.0853198e-005,
 -2.8878540e-005,
 -3.9992020e-005,
 -5.5381572e-005,
 -7.6691756e-005,
  -0.00010619896,
  -0.00014705353,
  -0.00020361416,
  -0.00028190913,
  -0.00039027152,
  -0.00054021234,
  -0.00074761674,
   -0.0010343765,
   -0.0014306041,
   -0.0019776123,
   -0.0027318744,
   -0.0037702007,
   -0.0051963365,
   -0.0071490559,
   -0.0098115020,
    -0.013420864,
    -0.018276322,
    -0.024741393,
    -0.033234627,
    -0.044200836,
    -0.058055984,
    -0.075105575,
    -0.095450827,
     -0.11891483,
     -0.14502864,
     -0.17309900,
     -0.20233808,
     -0.23199953,
     -0.26146829,
     -0.29028810,
     -0.31814628,
     -0.34484371,
     -0.37026666,
     -0.39436463,
     -0.41713328,
     -0.43860091,
     -0.45881778,
     -0.47784774,
     -0.49576189,
     -0.51263405,
     -0.52853755,
     -0.54354323,
     -0.55771814,
     -0.57112497,
     -0.58382172,
     -0.59586179,
     -0.60729409,
     -0.61816331,
     -0.62851025,
     -0.63837213,
     -0.64778287,
     -0.65677345,
     -0.66537214,
     -0.67360480,
     -0.68149508,
     -0.68906466,
     -0.69633344,
     -0.70331972,
     -0.71004030,
     -0.71651071,
     -0.72274526,
     -0.72875717,
     -0.73455870,
     -0.74016120,
     -0.74557521,
     -0.75081052,
     -0.75587624,
     -0.76078088,
     -0.76553235,
     -0.77013805,
 -6.4833985e-009,
 -8.9782214e-009,
 -1.2433196e-008,
 -1.7217893e-008,
 -2.3844184e-008,
 -3.3020914e-008,
 -4.5729556e-008,
 -6.3329636e-008,
 -8.7703735e-008,
 -1.2145901e-007,
 -1.6820631e-007,
 -2.3294594e-007,
 -3.2260293e-007,
 -4.4676760e-007,
 -6.1872141e-007,
 -8.5685757e-007,
 -1.1866486e-006,
 -1.6433705e-006,
 -2.2758764e-006,
 -3.1518210e-006,
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 -1.2958071e-009,
 -1.7906775e-009,
 -2.4760878e-009,
 -3.4253025e-009,
 -4.7397890e-009,
 -6.5601954e-009,
 -9.0813484e-009,
 -1.2572837e-008,
 -1.7408105e-008,
 -2.4104409e-008,
 -3.3377985e-008,
 -4.6220872e-008,
 -6.4006731e-008,
 -8.8638085e-008,
 -1.2274953e-007,
 -1.6998961e-007,
 -2.3541117e-007,
 -3.2601139e-007,
 -4.5148012e-007,
 -6.2523559e-007,
 -8.6585856e-007,
 -1.1990776e-006,
 -1.6605168e-006,
 -2.2994972e-006,
 -3.1842968e-006,
 -4.4094218e-006,
 -6.1056555e-006,
 -8.4539310e-006,
 -1.1704463e-005,
 -1.6203086e-005,
 -2.2427433e-005,
 -3.1036469e-005,
 -4.2938003e-005,
 -5.9380143e-005,
 -8.2074048e-005,
  -0.00011335664,
  -0.00015640232,
  -0.00021549105,
  -0.00029633393,
  -0.00040644301,
  -0.00055550318,
  -0.00075565594,
   -0.0010215337,
   -0.0013698039,
   -0.0018179376,
   -0.0023820051,
   -0.0030736261,
   -0.0038967940,
   -0.0048458749,
   -0.0059060816,
   -0.0070567021,
   -0.0082757721,
   -0.0095440306,
    -0.010846722,
    -0.012173373,
    -0.013516654,
    -0.014871268,
    -0.016233213,
    -0.017599358,
    -0.018967194,
    -0.020334677,
    -0.021700120,
    -0.023062123,
    -0.024419509,
    -0.025771289,
    -0.027116625,
    -0.028454808,
    -0.029785233,
    -0.031107387,
    -0.032420837,
    -0.033725211,
    -0.035020198,
    -0.036305536,
    -0.037581004,
    -0.038846420,
    -0.040101636,
    -0.041346531,
    -0.042581010,
    -0.043805002,
    -0.045018453,
    -0.046221329,
    -0.047413612,
    -0.048595295,
    -0.049766387,
    -0.050926904,
    -0.052076874,
    -0.053216335,
    -0.054345331,
    -0.055463911,
    -0.056572134,
    -0.057670062,
    -0.058757762,
    -0.059835306,
    -0.060902768,
    -0.061960228,
 -2.9560543e-010,
 -4.0490000e-010,
 -5.5624561e-010,
 -7.6579276e-010,
 -1.0560585e-009,
 -1.4579723e-009,
 -2.0146110e-009,
 -2.7855567e-009,
 -3.8531681e-009,
 -5.3317499e-009,
 -7.3792972e-009,
 -1.0215006e-008,
 -1.4142122e-008,
 -1.9580736e-008,
 -2.7112573e-008,
 -3.7543287e-008,
 -5.1988629e-008,
 -7.1993779e-008,
 -9.9698496e-008,
 -1.3806624e-007,
 -1.9120079e-007,
 -2.6478540e-007,
 -3.6669040e-007,
 -5.0781456e-007,
 -7.0325058e-007,
 -9.7389759e-007,
 -1.3486945e-006,
 -1.8677103e-006,
 -2.5864205e-006,
 -3.5816224e-006,
 -4.9596146e-006,
 -6.8674992e-006,
 -9.5087863e-006,
 -1.3164913e-005,
 -1.8224867e-005,
 -2.5225885e-005,
 -3.4909161e-005,
 -4.8295799e-005,
 -6.6789669e-005,
 -9.2315506e-005,
  -0.00012750194,
  -0.00017591969,
  -0.00024238316,
  -0.00033331685,
  -0.00045717156,
  -0.00062484322,
  -0.00084999294,
   -0.0011490869,
   -0.0015408855,
   -0.0020450611,
   -0.0026797210,
   -0.0034579790,
   -0.0043843829,
   -0.0054526599,
   -0.0066462435,
   -0.0079418968,
   -0.0093149637,
    -0.010743817,
    -0.012211887,
    -0.013707411,
    -0.015222155,
    -0.016750165,
    -0.018286940,
    -0.019828953,
    -0.021373375,
    -0.022917895,
    -0.024460608,
    -0.025999923,
    -0.027534503,
    -0.029063222,
    -0.030585120,
    -0.032099385,
    -0.033605322,
    -0.035102337,
    -0.036589926,
    -0.038067657,
    -0.039535164,
    -0.040992135,
    -0.042438308,
    -0.043873464,
    -0.045297420,
    -0.046710028,
    -0.048111166,
    -0.049500739,
    -0.050878677,
    -0.052244927,
    -0.053599455,
    -0.054942244,
    -0.056273290,
    -0.057592602,
    -0.058900201,
    -0.060196117,
    -0.061480389,
    -0.062753067,
    -0.064014204,
    -0.065263861,
    -0.066502107,
    -0.067729013,
    -0.068944655,
    -0.070149114};
#define Nterms            5
const double fit_arr[Ns][Nk][Nterms]={
 -2.7766853e-012,
  1.2869422e-010,
 -2.2173889e-009,
  1.6830761e-008,
 -4.7490873e-008,
     -0.33605695,
      0.96368599,
      -1.8317471,
       4.9060974,
      -7.8698730,
     -0.58579717,
       1.8127546,
      -4.4562073,
       14.887054,
      -26.323730,
     -0.78405485,
       2.5679009,
      -7.3600006,
       27.136047,
      -49.812378,
     -0.94808929,
       3.2460155,
      -10.325714,
       40.347046,
      -75.630371,
      -1.0877286,
       3.8602509,
      -13.253845,
       53.858582,
      -102.36060,
      -1.2091066,
       4.4208136,
      -16.097908,
       67.321167,
      -129.22046,
      -1.3163098,
       4.9357481,
      -18.837250,
       80.545776,
      -155.77515,
 -2.9359837e-012,
  1.3625721e-010,
 -2.3512239e-009,
  1.7876566e-008,
 -5.0534170e-008,
     -0.25084490,
      0.95998454,
      -2.3731995,
       6.0179901,
      -9.3836975,
     -0.44994166,
       1.8086560,
      -5.1017570,
       15.444336,
      -26.971375,
     -0.61463263,
       2.5674334,
      -7.9335785,
       26.554840,
      -48.938721,
     -0.75479786,
       3.2524748,
      -10.753288,
       38.468414,
      -73.262085,
     -0.87660519,
       3.8761015,
      -13.506439,
       50.705750,
      -98.802734,
     -0.98416463,
       4.4478688,
      -16.168015,
       62.997375,
      -124.89258,
      -1.0803522,
       4.9753160,
      -18.728134,
       75.189209,
      -151.13013,
 -2.2405218e-012,
  1.0404660e-010,
 -1.7961470e-009,
  1.3659423e-008,
 -3.8617424e-008,
     -0.20012233,
      0.95464516,
      -2.9508009,
       7.7952881,
      -11.847076,
     -0.36559752,
       1.8022749,
      -5.9260044,
       17.276093,
      -28.707336,
     -0.50637202,
       2.5632238,
      -8.8271713,
       27.542664,
      -48.368408,
     -0.62865673,
       3.2526174,
      -11.612267,
       38.112701,
      -69.588135,
     -0.73659079,
       3.8819888,
      -14.265747,
       48.719452,
      -91.637085,
     -0.83307110,
       4.4603293,
      -16.784756,
       59.212830,
      -114.07520,
     -0.92020349,
       4.9947698,
      -19.172607,
       69.508514,
      -136.63013,
 -1.9828946e-012,
  9.3118134e-011,
 -1.6242081e-009,
  1.2468479e-008,
 -3.5549410e-008,
     -0.16639251,
      0.94705510,
      -3.5141926,
       10.041481,
      -15.409088,
     -0.30790873,
       1.7934525,
      -6.8336258,
       20.376862,
      -32.839233,
     -0.43079949,
       2.5572193,
      -9.9395313,
       30.608017,
      -51.162109,
     -0.53923121,
       3.2519324,
      -12.832935,
       40.529053,
      -69.734680,
     -0.63611979,
       3.8880596,
      -15.523132,
       50.034698,
      -88.179382,
     -0.72358535,
       4.4738548,
      -18.022858,
       59.076630,
      -106.27423,
     -0.80321718,
       5.0159349,
      -20.345474,
       67.635925,
      -123.88745,
 -2.7956331e-012,
  1.2961042e-010,
 -2.2339396e-009,
  1.6963131e-008,
 -4.7886347e-008,
     -0.14228304,
      0.93661815,
      -4.0287466,
       12.489098,
      -19.736771,
     -0.26583641,
       1.7806025,
      -7.7373695,
       24.325371,
      -39.234497,
     -0.37484735,
       2.5473417,
      -11.144789,
       35.385635,
      -58.001831,
     -0.47224652,
       3.2486385,
      -14.273655,
       45.627014,
      -75.776001,
     -0.56016484,
       3.8937509,
      -17.146748,
       55.047729,
      -92.421631,
     -0.64019970,
       4.4900694,
      -19.785389,
       63.666565,
      -107.87561,
     -0.71357911,
       5.0436032,
      -22.209023,
       71.512878,
      -122.11609,
 -2.7956331e-012,
  1.2961042e-010,
 -2.2339396e-009,
  1.6963131e-008,
 -4.7886347e-008,
     -0.12414393,
      0.92310485,
      -4.4745550,
       14.912334,
      -24.385391,
     -0.23369673,
       1.7623850,
      -8.5708141,
       28.615005,
      -47.064911,
     -0.33159913,
       2.5307579,
      -12.323792,
       41.128693,
      -67.904053,
     -0.41998920,
       3.2383209,
      -15.765619,
       52.500168,
      -86.865601,
     -0.50047002,
       3.8931308,
      -18.925150,
       62.787643,
      -103.96667,
     -0.57427365,
       4.5017097,
      -21.827709,
       72.050766,
      -119.24768,
     -0.64236774,
       5.0694327,
      -24.495747,
       80.349976,
      -132.76788,
 -2.7956331e-012,
  1.2961042e-010,
 -2.2339396e-009,
  1.6963131e-008,
 -4.7886347e-008,
     -0.10996383,
      0.90664762,
      -4.8437481,
       17.159027,
      -28.981064,
     -0.20826419,
       1.7382818,
      -9.2940273,
       32.836029,
      -55.433884,
     -0.29704355,
       2.5056898,
      -13.391270,
       47.123459,
      -79.419250,
     -0.37790803,
       3.2174613,
      -17.170734,
       60.115295,
      -101.03073,
     -0.45209242,
       3.8805546,
      -20.663168,
       71.901840,
      -120.37671,
     -0.52056605,
       4.5006853,
      -23.895178,
       82.567062,
      -137.56769,
     -0.58410388,
       5.0826197,
      -26.890217,
       92.189102,
      -152.71423,
 -2.2471646e-012,
  1.0466442e-010,
 -1.8117994e-009,
  1.3813060e-008,
 -3.9139573e-008,
    -0.098545475,
      0.88761705,
      -5.1366763,
       19.144135,
      -33.268318,
     -0.18757654,
       1.7085178,
      -9.8896074,
       36.718689,
      -63.638077,
     -0.26870066,
       2.4717208,
      -14.299545,
       52.849434,
      -91.274414,
     -0.34315366,
       3.1845268,
      -18.401615,
       67.652802,
      -116.34494,
     -0.41190565,
       3.8529307,
      -22.226120,
       81.234344,
      -139.00998,
     -0.47573211,
       4.4819291,
      -25.799513,
       93.690536,
      -159.42340,
     -0.53526245,
       5.0757203,
      -29.144766,
       105.10809,
      -177.72729,
 -2.6207545e-012,
  1.2164288e-010,
 -2.0992262e-009,
  1.5959970e-008,
 -4.5108760e-008,
    -0.089132985,
      0.86649579,
      -5.3585424,
       20.831783,
      -37.098633,
     -0.17037468,
       1.6737919,
      -10.355905,
       40.116211,
      -71.216507,
     -0.24496069,
       2.4294571,
      -15.030782,
       57.991241,
      -102.57132,
     -0.31386101,
       3.1397058,
      -19.416467,
       74.580887,
      -131.36722,
     -0.37785087,
       3.8097090,
      -23.541777,
       89.996490,
      -157.79367,
     -0.43755944,
       4.4438170,
      -27.431787,
       104.33771,
      -182.02435,
     -0.49350424,
       5.0457299,
      -31.108507,
       117.69450,
      -204.22101,
 -1.9506611e-012,
  9.0966300e-011,
 -1.5763524e-009,
  1.2028835e-008,
 -3.4109638e-008,
    -0.081226213,
      0.84378971,
      -5.5169787,
       22.218416,
      -40.404556,
     -0.15581523,
       1.6350251,
      -10.700724,
       42.970383,
      -77.914215,
     -0.22473614,
       2.3800884,
      -15.586841,
       62.394470,
      -112.76804,
     -0.28876336,
       3.0842849,
      -20.206030,
       80.613792,
      -145.18469,
     -0.34852528,
       3.7520761,
      -24.584942,
       97.738152,
      -175.36340,
     -0.40453875,
       4.3872542,
      -28.746897,
       113.86620,
      -203.48669,
     -0.45723385,
       4.9930679,
      -32.712368,
       129.08603,
      -229.72055,
 -2.9517859e-012,
  1.3666176e-010,
 -2.3521022e-009,
  1.7833922e-008,
 -5.0268460e-008,
    -0.074481172,
      0.81997578,
      -5.6204574,
       23.319569,
      -43.173027,
     -0.14331237,
       1.5931841,
      -10.936679,
       45.280052,
      -83.624329,
     -0.20726676,
       2.3250329,
      -15.980841,
       66.014107,
      -121.59579,
     -0.26697167,
       3.0200681,
      -20.780778,
       85.639198,
      -157.30655,
     -0.32294292,
       3.6821461,
      -25.360759,
       104.26017,
      -190.95453,
     -0.37560967,
       4.3145730,
      -29.742073,
       121.97054,
      -222.72034,
     -0.42533263,
       4.9201987,
      -33.943396,
       138.85390,
      -252.76663,
 -2.3242511e-012,
  1.0794477e-010,
 -1.8637793e-009,
  1.4175745e-008,
 -4.0078824e-008,
    -0.068653408,
      0.79547569,
      -5.6773548,
       24.160816,
      -45.424538,
     -0.13244635,
       1.5491798,
      -11.078228,
       47.077301,
      -88.337654,
     -0.19200483,
       2.2657183,
      -16.231360,
       68.872787,
      -128.97282,
     -0.24784348,
       2.9489988,
      -21.161724,
       89.656677,
      -167.54063,
     -0.30039036,
       3.6023642,
      -25.891162,
       109.52624,
      -204.23093,
     -0.35000526,
       4.2286981,
      -30.438867,
       128.56837,
      -239.21570,
     -0.39699336,
       4.8305054,
      -34.821787,
       146.86083,
      -272.65073,
 -1.9506611e-012,
  9.0966300e-011,
 -1.5763524e-009,
  1.2028835e-008,
 -3.4109638e-008,
    -0.063564232,
      0.77064539,
      -5.6954315,
       24.771858,
      -47.198368,
     -0.12290810,
       1.5038146,
      -11.139794,
       48.410839,
      -92.102470,
     -0.17854495,
       2.2034498,
      -16.358587,
       71.029694,
      -134.93153,
     -0.23090171,
       2.8729235,
      -21.374066,
       92.728363,
      -175.88261,
     -0.28033709,
       3.5151398,
      -26.205721,
       113.59577,
      -215.13310,
     -0.32715534,
       4.1326207,
      -30.870750,
       133.71132,
      -252.84305,
     -0.37161658,
       4.7275664,
      -35.384370,
       153.14587,
      -289.15744,
 -2.5057725e-012,
  1.1653012e-010,
 -2.0141451e-009,
  1.5332543e-008,
 -4.3378561e-008,
    -0.059079832,
      0.74577713,
      -5.6816335,
       25.183113,
      -48.542873,
     -0.11446455,
       1.4577674,
      -11.134885,
       49.336273,
      -94.999153,
     -0.16657990,
       2.1393620,
      -16.382279,
       72.561241,
      -139.57077,
     -0.21578355,
       2.7934821,
      -21.443572,
       94.948425,
      -182.43901,
     -0.26237877,
       3.4226599,
      -26.336087,
       116.57806,
      -223.76651,
     -0.30662478,
       4.0291041,
      -31.075133,
       137.52168,
      -263.69980,
     -0.34874494,
       4.6147539,
      -35.674307,
       157.84361,
      -302.37149,
 -2.5057725e-012,
  1.1653012e-010,
 -2.0141451e-009,
  1.5332543e-008,
 -4.3378561e-008,
    -0.055097810,
      0.72110331,
      -5.6419959,
       25.423559,
      -49.508888,
     -0.10693620,
       1.4115930,
      -11.075565,
       49.909378,
      -97.121330,
     -0.15587181,
       2.0744003,
      -16.320586,
       73.548714,
      -143.02098,
     -0.20220695,
       2.7120656,
      -21.394512,
       96.422455,
      -187.37233,
     -0.24620003,
       3.3268036,
      -26.312714,
       118.60252,
      -230.32274,
     -0.28807359,
       3.9205567,
      -31.088831,
       140.15320,
      -272.00514,
     -0.32802055,
       4.4950368,
      -35.734942,
       161.13196,
      -312.53903,
 -2.3621467e-012,
  1.0977718e-010,
 -1.8968806e-009,
  1.4440486e-008,
 -4.0869772e-008,
    -0.051538335,
      0.69680456,
      -5.5816913,
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extern "C" double RFactorNApprox(double tau, int s, int k)
{
 if (s<s_arr[0] || s>s_arr[Ns-1] || k<k_arr[0] || k>k_arr[Nk-1]) return dNaN;
 else
 {
  double logtau=log(tau);
  int si=s-s_arr[0];
  int ki=k-k_arr[0];

  double logR, dy;

  if (logtau<logtau1_arr[0]) 
   logR=logR1_arr[si][ki][0]+(logR1_arr[si][ki][1]-logR1_arr[si][ki][0])*
        (logtau-logtau1_arr[0])/(logtau1_arr[1]-logtau1_arr[0]);
  else if (logtau<logtau1_arr[Ntau1-1])
  {
   int ti1=int((logtau-logtau1_arr[0])/(logtau1_arr[1]-logtau1_arr[0])+0.5)-2;
   if (ti1<0) ti1=0;
   if (ti1>(Ntau1-5)) ti1=Ntau1-5;
   polint(logtau1_arr+ti1, logR1_arr[si][ki]+ti1, 5, logtau, &logR, &dy);
  }
  else 
  {
   double a=1.0;
   logR=0;
   for (int i=0; i<Nterms; i++)
   {
	logR+=fit_arr[si][ki][i]*a;
	a/=logtau;
   }
  }

  return exp(logR);
 }
}