/***********************************************************
* Smithsonian Astrophysical Observatory
* Submillimeter Receiver Laboratory
* am
*
* specfunc.c                    S. Paine rev. 2018 August 16
*
* Special functions.
************************************************************/

#include <math.h>


/***********************************************************
* double am_exp(double x)
*
* Purpose:
*   A wrapper to avoid arguments to exp() that produce
*   denormal results.
*
*   The smallest normalized IEEE 754 double is
*
*     eps = 2^-1022 = 2.2250738585072014e-308
*
*     log(eps) = -1022 * log(2) = -708.3964185322641
*
*  and the smallest denormal double is
*
*    eps' = 2^-(1022 + 52) = 5e-324
*
*    log(eps') = -(1022 + 52) * log(2) = -744.4400719213812
*
*  The exp() implementations in both gcc and pgcc take about
*  an order of magnitude longer for log(eps') <~ x < log(eps)
*  than for x outside this range.  Interestingly, both take
*  about the same amount of time for x <~ log(eps') and for
*  x > log(eps), indicating that the zero results returned
*  for x <~ log(eps') are computed rather than based on a
*  simple test.  Presumably this is an optimization to
*  slightly improve speed for x > log(eps).  The choice of
*  whether to use this function or simply exp() in various
*  parts of the am code depends on whether or not a
*  significant fraction of arguments that will produce
*  denormal results is expected.
*
* Arguments:
*   double x
*
* Return:
*   exp(x), or zero if x < log(eps)
************************************************************/

double am_exp(double x)
{
    return x < -708.3964185322641 ? 0.0 : exp(x);
}   /* am_exp() */


/***********************************************************
* double am_K0(double x)
*
* Purpose:
*   Computes the modified Bessel function K0(x), over the range
*   0 < x < inf.  To save time, no argument checking is done.
*
*   For 0 < x < q, where q = 0.5, the function is approximated by
*
*       K0(x) = -log(x) + y(x),
*
*   where y(x) is computed by cubic spline interpolation of a lookup
*   table.  For x >= q, the function is approximated by
*
*       K0(x) = v(u),
*
*   where u = 1/x, and v(u) is again computed by cubic spline
*   interpolation of a lookup table.
*
*   The lookup tables were computed using Mathcad 7's implementation
*   of K0(), then the accuracy of the interpolation was evaluated on
*   a finer mesh.  For x < q, the worst-case _normalized_ error is
*   about 2e-9, at x = 5e-4, where K0(x) = 7.7.  For x > q, the worst-
*   case _absolute_ error is about 2.5e-10, at x = 10, where
*   K0(x) = 1.8e-5 (i.e. a normalized error of about 1e-5.)
*
* Arguments:
*   double x
*
* Return:
*   K0(x)
************************************************************/

/*
 * The lookup tables below all have n = 512 points.  Note that the
 * table for x > q was computed starting at x = q - 1.e-6, to
 * place the point x = q inside the interpolation table.
 */

#define K0_XSCALE   1022.0              /* (n - 1) / q */
#define K0_USCALE   255.499489000000    /* (n - 1) / (1 / (q + 1.e-6)) */

/*
 * Lookup tables for 0 < x < q.  x values are scaled so that the table
 * abscissas are integers from 0 to 511.
 */

static const double K0_y[] = {
1.15931515658412e-01, 1.15933441357801e-01, 1.15938554830850e-01, 1.15946480358703e-01,
1.15957017861527e-01, 1.15970027621915e-01, 1.15985401912574e-01, 1.16003052971787e-01,
1.16022906722437e-01, 1.16044899064176e-01, 1.16068973497634e-01, 1.16095079509194e-01,
1.16123171422322e-01, 1.16153207551237e-01, 1.16185149559190e-01, 1.16218961960266e-01,
1.16254611724788e-01, 1.16292067961477e-01, 1.16331301657607e-01, 1.16372285463881e-01,
1.16414993514298e-01, 1.16459401273812e-01, 1.16505485408331e-01, 1.16553223672907e-01,
1.16602594814865e-01, 1.16653578489310e-01, 1.16706155185014e-01, 1.16760306159018e-01,
1.16816013378657e-01, 1.16873259469922e-01, 1.16932027671250e-01, 1.16992301792033e-01,
1.17054066175200e-01, 1.17117305663377e-01, 1.17182005568159e-01, 1.17248151642151e-01,
1.17315730053429e-01, 1.17384727362171e-01, 1.17455130499199e-01, 1.17526926746248e-01,
1.17600103717769e-01, 1.17674649344114e-01, 1.17750551855964e-01, 1.17827799769891e-01,
1.17906381874935e-01, 1.17986287220105e-01, 1.18067505102722e-01, 1.18150025057536e-01,
1.18233836846546e-01, 1.18318930449448e-01, 1.18405296054699e-01, 1.18492924051095e-01,
1.18581805019872e-01, 1.18671929727254e-01, 1.18763289117431e-01, 1.18855874305930e-01,
1.18949676573353e-01, 1.19044687359445e-01, 1.19140898257492e-01, 1.19238301008996e-01,
1.19336887498632e-01, 1.19436649749451e-01, 1.19537579918339e-01, 1.19639670291667e-01,
1.19742913281184e-01, 1.19847301420075e-01, 1.19952827359220e-01, 1.20059483863618e-01,
1.20167263808970e-01, 1.20276160178423e-01, 1.20386166059442e-01, 1.20497274640829e-01,
1.20609479209866e-01, 1.20722773149574e-01, 1.20837149936089e-01, 1.20952603136141e-01,
1.21069126404643e-01, 1.21186713482362e-01, 1.21305358193698e-01, 1.21425054444531e-01,
1.21545796220165e-01, 1.21667577583342e-01, 1.21790392672332e-01, 1.21914235699093e-01,
1.22039100947493e-01, 1.22164982771609e-01, 1.22291875594069e-01, 1.22419773904469e-01,
1.22548672257827e-01, 1.22678565273109e-01, 1.22809447631790e-01, 1.22941314076467e-01,
1.23074159409525e-01, 1.23207978491839e-01, 1.23342766241517e-01, 1.23478517632690e-01,
1.23615227694334e-01, 1.23752891509136e-01, 1.23891504212385e-01, 1.24031060990908e-01,
1.24171557082032e-01, 1.24312987772573e-01, 1.24455348397871e-01, 1.24598634340834e-01,
1.24742841031023e-01, 1.24887963943759e-01, 1.25033998599256e-01, 1.25180940561778e-01,
1.25328785438820e-01, 1.25477528880316e-01, 1.25627166577856e-01, 1.25777694263945e-01,
1.25929107711261e-01, 1.26081402731947e-01, 1.26234575176917e-01, 1.26388620935177e-01,
1.26543535933171e-01, 1.26699316134141e-01, 1.26855957537495e-01, 1.27013456178207e-01,
1.27171808126224e-01, 1.27331009485880e-01, 1.27491056395338e-01, 1.27651945026038e-01,
1.27813671582161e-01, 1.27976232300107e-01, 1.28139623447980e-01, 1.28303841325093e-01,
1.28468882261477e-01, 1.28634742617410e-01, 1.28801418782951e-01, 1.28968907177480e-01,
1.29137204249265e-01, 1.29306306475021e-01, 1.29476210359488e-01, 1.29646912435019e-01,
1.29818409261174e-01, 1.29990697424319e-01, 1.30163773537251e-01, 1.30337634238804e-01,
1.30512276193490e-01, 1.30687696091130e-01, 1.30863890646501e-01, 1.31040856598987e-01,
1.31218590712243e-01, 1.31397089773855e-01, 1.31576350595020e-01, 1.31756370010220e-01,
1.31937144876916e-01, 1.32118672075237e-01, 1.32300948507677e-01, 1.32483971098809e-01,
1.32667736794986e-01, 1.32852242564063e-01, 1.33037485395123e-01, 1.33223462298195e-01,
1.33410170303999e-01, 1.33597606463674e-01, 1.33785767848529e-01, 1.33974651549783e-01,
1.34164254678326e-01, 1.34354574364474e-01, 1.34545607757727e-01, 1.34737352026538e-01,
1.34929804358089e-01, 1.35122961958053e-01, 1.35316822050389e-01, 1.35511381877111e-01,
1.35706638698081e-01, 1.35902589790802e-01, 1.36099232450207e-01, 1.36296563988460e-01,
1.36494581734757e-01, 1.36693283035130e-01, 1.36892665252258e-01, 1.37092725765273e-01,
1.37293461969580e-01, 1.37494871276675e-01, 1.37696951113963e-01, 1.37899698924582e-01,
1.38103112167233e-01, 1.38307188316008e-01, 1.38511924860221e-01, 1.38717319304249e-01,
1.38923369167361e-01, 1.39130071983569e-01, 1.39337425301462e-01, 1.39545426684059e-01,
1.39754073708652e-01, 1.39963363966662e-01, 1.40173295063485e-01, 1.40383864618354e-01,
1.40595070264194e-01, 1.40806909647480e-01, 1.41019380428102e-01, 1.41232480279227e-01,
1.41446206887166e-01, 1.41660557951244e-01, 1.41875531183666e-01, 1.42091124309392e-01,
1.42307335066012e-01, 1.42524161203620e-01, 1.42741600484692e-01, 1.42959650683966e-01,
1.43178309588324e-01, 1.43397574996675e-01, 1.43617444719838e-01, 1.43837916580432e-01,
1.44058988412759e-01, 1.44280658062698e-01, 1.44502923387597e-01, 1.44725782256161e-01,
1.44949232548350e-01, 1.45173272155276e-01, 1.45397898979095e-01, 1.45623110932911e-01,
1.45848905940675e-01, 1.46075281937082e-01, 1.46302236867483e-01, 1.46529768687779e-01,
1.46757875364333e-01, 1.46986554873876e-01, 1.47215805203411e-01, 1.47445624350129e-01,
1.47676010321312e-01, 1.47906961134253e-01, 1.48138474816158e-01, 1.48370549404072e-01,
1.48603182944785e-01, 1.48836373494753e-01, 1.49070119120012e-01, 1.49304417896099e-01,
1.49539267907973e-01, 1.49774667249929e-01, 1.50010614025525e-01, 1.50247106347505e-01,
1.50484142337717e-01, 1.50721720127045e-01, 1.50959837855324e-01, 1.51198493671279e-01,
1.51437685732443e-01, 1.51677412205085e-01, 1.51917671264148e-01, 1.52158461093167e-01,
1.52399779884208e-01, 1.52641625837797e-01, 1.52883997162851e-01, 1.53126892076615e-01,
1.53370308804591e-01, 1.53614245580477e-01, 1.53858700646100e-01, 1.54103672251355e-01,
1.54349158654139e-01, 1.54595158120291e-01, 1.54841668923529e-01, 1.55088689345392e-01,
1.55336217675177e-01, 1.55584252209881e-01, 1.55832791254142e-01, 1.56081833120182e-01,
1.56331376127748e-01, 1.56581418604059e-01, 1.56831958883745e-01, 1.57082995308795e-01,
1.57334526228502e-01, 1.57586549999406e-01, 1.57839064985245e-01, 1.58092069556901e-01,
1.58345562092342e-01, 1.58599540976581e-01, 1.58854004601613e-01, 1.59108951366375e-01,
1.59364379676685e-01, 1.59620287945205e-01, 1.59876674591382e-01, 1.60133538041404e-01,
1.60390876728149e-01, 1.60648689091144e-01, 1.60906973576511e-01, 1.61165728636923e-01,
1.61424952731560e-01, 1.61684644326063e-01, 1.61944801892486e-01, 1.62205423909255e-01,
1.62466508861122e-01, 1.62728055239123e-01, 1.62990061540536e-01, 1.63252526268831e-01,
1.63515447933639e-01, 1.63778825050701e-01, 1.64042656141832e-01, 1.64306939734877e-01,
1.64571674363673e-01, 1.64836858568006e-01, 1.65102490893573e-01, 1.65368569891946e-01,
1.65635094120525e-01, 1.65902062142508e-01, 1.66169472526847e-01, 1.66437323848212e-01,
1.66705614686957e-01, 1.66974343629076e-01, 1.67243509266174e-01, 1.67513110195423e-01,
1.67783145019535e-01, 1.68053612346718e-01, 1.68324510790645e-01, 1.68595838970420e-01,
1.68867595510540e-01, 1.69139779040863e-01, 1.69412388196574e-01, 1.69685421618151e-01,
1.69958877951334e-01, 1.70232755847087e-01, 1.70507053961569e-01, 1.70781770956101e-01,
1.71056905497136e-01, 1.71332456256223e-01, 1.71608421909978e-01, 1.71884801140054e-01,
1.72161592633107e-01, 1.72438795080770e-01, 1.72716407179617e-01, 1.72994427631137e-01,
1.73272855141705e-01, 1.73551688422548e-01, 1.73830926189721e-01, 1.74110567164073e-01,
1.74390610071225e-01, 1.74671053641535e-01, 1.74951896610070e-01, 1.75233137716586e-01,
1.75514775705491e-01, 1.75796809325823e-01, 1.76079237331220e-01, 1.76362058479896e-01,
1.76645271534612e-01, 1.76928875262651e-01, 1.77212868435789e-01, 1.77497249830272e-01,
1.77782018226789e-01, 1.78067172410449e-01, 1.78352711170750e-01, 1.78638633301559e-01,
1.78924937601086e-01, 1.79211622871856e-01, 1.79498687920690e-01, 1.79786131558677e-01,
1.80073952601150e-01, 1.80362149867664e-01, 1.80650722181973e-01, 1.80939668372000e-01,
1.81228987269824e-01, 1.81518677711649e-01, 1.81808738537784e-01, 1.82099168592620e-01,
1.82389966724608e-01, 1.82681131786237e-01, 1.82972662634008e-01, 1.83264558128420e-01,
1.83556817133939e-01, 1.83849438518983e-01, 1.84142421155899e-01, 1.84435763920941e-01,
1.84729465694246e-01, 1.85023525359822e-01, 1.85317941805517e-01, 1.85612713923003e-01,
1.85907840607760e-01, 1.86203320759046e-01, 1.86499153279887e-01, 1.86795337077048e-01,
1.87091871061021e-01, 1.87388754146001e-01, 1.87685985249866e-01, 1.87983563294163e-01,
1.88281487204081e-01, 1.88579755908439e-01, 1.88878368339664e-01, 1.89177323433772e-01,
1.89476620130350e-01, 1.89776257372538e-01, 1.90076234107012e-01, 1.90376549283961e-01,
1.90677201857075e-01, 1.90978190783524e-01, 1.91279515023940e-01, 1.91581173542402e-01,
1.91883165306413e-01, 1.92185489286892e-01, 1.92488144458146e-01, 1.92791129797862e-01,
1.93094444287083e-01, 1.93398086910199e-01, 1.93702056654920e-01, 1.94006352512271e-01,
1.94310973476566e-01, 1.94615918545397e-01, 1.94921186719617e-01, 1.95226777003322e-01,
1.95532688403837e-01, 1.95838919931699e-01, 1.96145470600643e-01, 1.96452339427584e-01,
1.96759525432604e-01, 1.97067027638935e-01, 1.97374845072942e-01, 1.97682976764113e-01,
1.97991421745039e-01, 1.98300179051403e-01, 1.98609247721960e-01, 1.98918626798528e-01,
1.99228315325970e-01, 1.99538312352181e-01, 1.99848616928070e-01, 2.00159228107553e-01,
2.00470144947533e-01, 2.00781366507883e-01, 2.01092891851442e-01, 2.01404720043992e-01,
2.01716850154250e-01, 2.02029281253849e-01, 2.02342012417329e-01, 2.02655042722121e-01,
2.02968371248535e-01, 2.03281997079744e-01, 2.03595919301776e-01, 2.03910137003493e-01,
2.04224649276588e-01, 2.04539455215560e-01, 2.04854553917713e-01, 2.05169944483134e-01,
2.05485626014687e-01, 2.05801597617995e-01, 2.06117858401432e-01, 2.06434407476105e-01,
2.06751243955849e-01, 2.07068366957208e-01, 2.07385775599427e-01, 2.07703469004437e-01,
2.08021446296846e-01, 2.08339706603924e-01, 2.08658249055592e-01, 2.08977072784412e-01,
2.09296176925574e-01, 2.09615560616883e-01, 2.09935222998750e-01, 2.10255163214178e-01,
2.10575380408752e-01, 2.10895873730627e-01, 2.11216642330519e-01, 2.11537685361691e-01,
2.11859001979940e-01, 2.12180591343592e-01, 2.12502452613488e-01, 2.12824584952970e-01,
2.13146987527875e-01, 2.13469659506521e-01, 2.13792600059698e-01, 2.14115808360657e-01,
2.14439283585099e-01, 2.14763024911165e-01, 2.15087031519423e-01, 2.15411302592863e-01,
2.15735837316883e-01, 2.16060634879277e-01, 2.16385694470229e-01, 2.16711015282301e-01,
2.17036596510423e-01, 2.17362437351881e-01, 2.17688537006312e-01, 2.18014894675689e-01,
2.18341509564314e-01, 2.18668380878808e-01, 2.18995507828099e-01, 2.19322889623418e-01,
2.19650525478281e-01, 2.19978414608487e-01, 2.20306556232107e-01, 2.20634949569470e-01,
2.20963593843159e-01, 2.21292488277998e-01, 2.21621632101048e-01, 2.21951024541591e-01,
2.22280664831124e-01, 2.22610552203353e-01, 2.22940685894178e-01, 2.23271065141690e-01,
2.23601689186156e-01, 2.23932557270017e-01, 2.24263668637874e-01, 2.24595022536478e-01,
2.24926618214730e-01, 2.25258454923663e-01, 2.25590531916435e-01, 2.25922848448327e-01,
2.26255403776728e-01, 2.26588197161127e-01, 2.26921227863108e-01, 2.27254495146339e-01,
2.27587998276566e-01, 2.27921736521599e-01, 2.28255709151313e-01, 2.28589915437633e-01,
2.28924354654527e-01, 2.29259026077999e-01, 2.29593928986082e-01, 2.29929062658827e-01,
2.30264426378298e-01, 2.30600019428564e-01, 2.30935841095687e-01, 2.31271890667720e-01,
};

static const double K0_y2[] = {
0.00000000000000e+00, 5.01569284281619e-07, 4.69431471523859e-07, 4.32759632859149e-07,
4.11504968462168e-07, 3.93478057293444e-07, 3.79113073501308e-07, 3.66838202833824e-07,
3.56225551522711e-07, 3.46850680182296e-07, 3.38463447227807e-07, 3.30873632208974e-07,
3.23943592460480e-07, 3.17567784535869e-07, 3.11664307984451e-07, 3.06168105687186e-07,
3.01026716432587e-07, 2.96197194215472e-07, 2.91643948559555e-07, 2.87337155462877e-07,
2.83251573052882e-07, 2.79365648906495e-07, 2.75660836354172e-07, 2.72121062159997e-07,
2.68732297201922e-07, 2.65482236570545e-07, 2.62360015421376e-07, 2.59356001464737e-07,
2.56461613745663e-07, 2.53669169236278e-07, 2.50971772188500e-07, 2.48363197811747e-07,
2.45837820727340e-07, 2.43390528530966e-07, 2.41016670574301e-07, 2.38711998445590e-07,
2.36472622642878e-07, 2.34294974062002e-07, 2.32175767780462e-07, 2.30111975935674e-07,
2.28100800121453e-07, 2.26139647275369e-07, 2.24226115621097e-07, 2.22357968430245e-07,
2.20533126911355e-07, 2.18749649396914e-07, 2.17005723118489e-07, 2.15299655302615e-07,
2.13629851730987e-07, 2.11994829247295e-07, 2.10393180508361e-07, 2.08823593670894e-07,
2.07284825768730e-07, 2.05775708248787e-07, 2.04295136350967e-07, 2.02842068305024e-07,
2.01415514294178e-07, 2.00014543656220e-07, 1.98638266671385e-07, 1.97285846030864e-07,
1.95956480721220e-07, 1.94649415497455e-07, 1.93363924879489e-07, 1.92099325948793e-07,
1.90854960040763e-07, 1.89630206993321e-07, 1.88424467332329e-07, 1.87237175316488e-07,
1.86067786332716e-07, 1.84915780074858e-07, 1.83780659545293e-07, 1.82661949649351e-07,
1.81559192269711e-07, 1.80471951831277e-07, 1.79399807293150e-07, 1.78342356855488e-07,
1.77299213801434e-07, 1.76270006432134e-07, 1.75254376711587e-07, 1.74251983087677e-07,
1.73262492783644e-07, 1.72285588938991e-07, 1.71320964409307e-07, 1.70368323438866e-07,
1.69427382058591e-07, 1.68497863933417e-07, 1.67579506360820e-07, 1.66672050199300e-07,
1.65775251063293e-07, 1.64888869039926e-07, 1.64012671981756e-07, 1.63146439280378e-07,
1.62289952805135e-07, 1.61443004505675e-07, 1.60605392826580e-07, 1.59776919676335e-07,
1.58957399031384e-07, 1.58146642870426e-07, 1.57344476414663e-07, 1.56550725427377e-07,
1.55765222021397e-07, 1.54987804787795e-07, 1.54218315138179e-07, 1.53456599816398e-07,
1.52702511170785e-07, 1.51955903109382e-07, 1.51216636792752e-07, 1.50484574786080e-07,
1.49759584991204e-07, 1.49041537871808e-07, 1.48330308735653e-07, 1.47625775377244e-07,
1.46927817675425e-07, 1.46236322892597e-07, 1.45551175094306e-07, 1.44872266858584e-07,
1.44199491440706e-07, 1.43532742864901e-07, 1.42871921616389e-07, 1.42216929101003e-07,
1.41567666795183e-07, 1.40924042521850e-07, 1.40285964404562e-07, 1.39653342343725e-07,
1.39026089933948e-07, 1.38404120647478e-07, 1.37787353633588e-07, 1.37175704995737e-07,
1.36569097787708e-07, 1.35967453400436e-07, 1.35370695590457e-07, 1.34778752749255e-07,
1.34191549682395e-07, 1.33609018683727e-07, 1.33031087884338e-07, 1.32457692801729e-07,
1.31888764442699e-07, 1.31324240917725e-07, 1.30764057305472e-07, 1.30208152153854e-07,
1.29656466044197e-07, 1.29108938168977e-07, 1.28565511908796e-07, 1.28026130157582e-07,
1.27490736898515e-07, 1.26959278461680e-07, 1.26431701136387e-07, 1.25907953024947e-07,
1.25387982790005e-07, 1.24871740146888e-07, 1.24359176923254e-07, 1.23850243438348e-07,
1.23344893710700e-07, 1.22843082236880e-07, 1.22344760344496e-07, 1.21849888450345e-07,
1.21358417986294e-07, 1.20870310359344e-07, 1.20385520041711e-07, 1.19904008833521e-07,
1.19425734365705e-07, 1.18950657844898e-07, 1.18478739447951e-07, 1.18009943003764e-07,
1.17544227644610e-07, 1.17081560309751e-07, 1.16621902057270e-07, 1.16165217894615e-07,
1.15711474459263e-07, 1.15260635246689e-07, 1.14812668473099e-07, 1.14367539492360e-07,
1.13925217056296e-07, 1.13485668513117e-07, 1.13048862761397e-07, 1.12614768342763e-07,
1.12183356118752e-07, 1.11754595133636e-07, 1.11328456050170e-07, 1.10904911313734e-07,
1.10483931282068e-07, 1.10065487773815e-07, 1.09649555512987e-07, 1.09236104578909e-07,
1.08825110954325e-07, 1.08416546752022e-07, 1.08010387443954e-07, 1.07606607151002e-07,
1.07205180928954e-07, 1.06806084775719e-07, 1.06409293982613e-07, 1.06014785281106e-07,
1.05622535233635e-07, 1.05232520304752e-07, 1.04844718851839e-07, 1.04459107754056e-07,
1.04075665024038e-07, 1.03694369837591e-07, 1.03315199803205e-07, 1.02938135192979e-07,
1.02563153853223e-07, 1.02190236895038e-07, 1.01819362789763e-07, 1.01450513528231e-07,
1.01083667878703e-07, 1.00718807540949e-07, 1.00355913926929e-07, 9.99949673344610e-08,
9.96359501412061e-08, 9.92788444029792e-08, 9.89236316051824e-08, 9.85702945044465e-08,
9.82188160058377e-08, 9.78691778155850e-08, 9.75213651766083e-08, 9.71753594877294e-08,
9.68311444395541e-08, 9.64887059491667e-08, 9.61480251752465e-08, 9.58090885372959e-08,
9.54718792705606e-08, 9.51363825353756e-08, 9.48025834168670e-08, 9.44704662640858e-08,
9.41400173353693e-08, 9.38112210950104e-08, 9.34840637214799e-08, 9.31585316596522e-08,
9.28346094627871e-08, 9.25122847653522e-08, 9.21915429842483e-08, 9.18723717727228e-08,
9.15547562750508e-08, 9.12386849941571e-08, 9.09241443891247e-08, 9.06111210728179e-08,
9.02996037529508e-08, 8.99895785992617e-08, 8.96810345094711e-08, 8.93739586686852e-08,
8.90683390538164e-08, 8.87641646296570e-08, 8.84614222822079e-08, 8.81601022279544e-08,
8.78601914338400e-08, 8.75616796511090e-08, 8.72645554046823e-08, 8.69688077861612e-08,
8.66744259569722e-08, 8.63813986766492e-08, 8.60897164645165e-08, 8.57993674214767e-08,
8.55103424553024e-08, 8.52226305480913e-08, 8.49362220250570e-08, 8.46511062071148e-08,
8.43672744231238e-08, 8.40847154153574e-08, 8.38034209354183e-08, 8.35233801675607e-08,
8.32445848931661e-08, 8.29670246235706e-08, 8.26906913563619e-08, 8.24155745211924e-08,
8.21416664482231e-08, 8.18689575389430e-08, 8.15974390122178e-08, 8.13271020783460e-08,
8.10579389408745e-08, 8.07899393932369e-08, 8.05230969910898e-08, 8.02574015330951e-08,
7.99928463121096e-08, 7.97294223948115e-08, 7.94671213734163e-08, 7.92059362964371e-08,
7.89458580805067e-08, 7.86868800505440e-08, 7.84289935813202e-08, 7.81721914431075e-08,
7.79164658829468e-08, 7.76618098453028e-08, 7.74082153404436e-08, 7.71556749755103e-08,
7.69041825688827e-08, 7.66537296057380e-08, 7.64043094755758e-08, 7.61559156128798e-08,
7.59085404780973e-08, 7.56621770521683e-08, 7.54168194285439e-08, 7.51724598387638e-08,
7.49290919645195e-08, 7.46867093235659e-08, 7.44453055274306e-08, 7.42048735323981e-08,
7.39654072676396e-08, 7.37269005346476e-08, 7.34893466727433e-08, 7.32527396653430e-08,
7.30170733800560e-08, 7.27823417256689e-08, 7.25485381179773e-08, 7.23156576815182e-08,
7.20836934177021e-08, 7.18526397826331e-08, 7.16224915335707e-08, 7.13932418786819e-08,
7.11648859245458e-08, 7.09374176181668e-08, 7.07108316480345e-08, 7.04851224505840e-08,
7.02602838408055e-08, 7.00363117053899e-08, 6.98131989286058e-08, 6.95909425595510e-08,
6.93695342060797e-08, 6.91489717519158e-08, 6.89292476294034e-08, 6.87103580321710e-08,
6.84922977757407e-08, 6.82750605401951e-08, 6.80586434829912e-08, 6.78430396472676e-08,
6.76282450640540e-08, 6.74142552546066e-08, 6.72010641252512e-08, 6.69886681109154e-08,
6.67770622524787e-08, 6.65662406416070e-08, 6.63562010065579e-08, 6.61469361381739e-08,
6.59384433940475e-08, 6.57307170162385e-08, 6.55237538131163e-08, 6.53175474401479e-08,
6.51120956028956e-08, 6.49073925073614e-08, 6.47034340920423e-08, 6.45002161956850e-08,
6.42977353219438e-08, 6.40959854145926e-08, 6.38949639968154e-08, 6.36946663819543e-08,
6.34950880362827e-08, 6.32962253580567e-08, 6.30980741953397e-08, 6.29006305547598e-08,
6.27038901368348e-08, 6.25078499300033e-08, 6.23125042975777e-08, 6.21178517084280e-08,
6.19238859381483e-08, 6.17306049937828e-08, 6.15380041977694e-08, 6.13460796063612e-08,
6.11548288015136e-08, 6.09642460812712e-08, 6.07743298041032e-08, 6.05850746965640e-08,
6.03964786249712e-08, 6.02085365237087e-08, 6.00212465860613e-08, 5.98346031188931e-08,
5.96486049442881e-08, 5.94632469239247e-08, 5.92785263640981e-08, 5.90944398600690e-08,
5.89109837404844e-08, 5.87281552233032e-08, 5.85459497901619e-08, 5.83643658700506e-08,
5.81833987222499e-08, 5.80030457880085e-08, 5.78233038353938e-08, 5.76441696991401e-08,
5.74656396212953e-08, 5.72877114818524e-08, 5.71103811985129e-08, 5.69336465703297e-08,
5.67575032749330e-08, 5.65819500415780e-08, 5.64069819537371e-08, 5.62325976327825e-08,
5.60587928548088e-08, 5.58855654659623e-08, 5.57129124293740e-08, 5.55408301717823e-08,
5.53693170382890e-08, 5.51983686778275e-08, 5.50279838324804e-08, 5.48581577851519e-08,
5.46888902340386e-08, 5.45201755571308e-08, 5.43520135626538e-08, 5.41843996485083e-08,
5.40173319867622e-08, 5.38508081693667e-08, 5.36848244463933e-08, 5.35193791297692e-08,
5.33544689549484e-08, 5.31900921258641e-08, 5.30262447694532e-08, 5.28629256333102e-08,
5.27001314986889e-08, 5.25378591735008e-08, 5.23761078804786e-08, 5.22148734846831e-08,
5.20541539852577e-08, 5.18939471986912e-08, 5.17342506482312e-08, 5.15750615474097e-08,
5.14163775316399e-08, 5.12581964128371e-08, 5.11005158742288e-08, 5.09433334932018e-08,
5.07866461779481e-08, 5.06304530641683e-08, 5.04747503757939e-08, 5.03195366508966e-08,
5.01648097448945e-08, 5.00105663753670e-08, 4.98568054962999e-08, 4.97035240270518e-08,
4.95507200151248e-08, 4.93983915835872e-08, 4.92465357581656e-08, 4.90951514358969e-08,
4.89442351227214e-08, 4.87937860216517e-08, 4.86438011557570e-08, 4.84942783527589e-08,
4.83452164001146e-08, 4.81966118841779e-08, 4.80484639069091e-08, 4.79007697041507e-08,
4.77535275748288e-08, 4.76067354300551e-08, 4.74603906699145e-08, 4.73144925713012e-08,
4.71690378557919e-08, 4.70240250391077e-08, 4.68794524566015e-08, 4.67353174819779e-08,
4.65916189623893e-08, 4.64483541435140e-08, 4.63055217617877e-08, 4.61631197448047e-08,
4.60211457663656e-08, 4.58795986581533e-08, 4.57384760937623e-08, 4.55977761126342e-08,
4.54574974481106e-08, 4.53176375794653e-08, 4.51781951997196e-08, 4.50391680655067e-08,
4.49005550219755e-08, 4.47623533839794e-08, 4.46245623904132e-08, 4.44871793331498e-08,
4.43502030382374e-08, 4.42136316947591e-08, 4.40774633952607e-08, 4.39416965892680e-08,
4.38063293941242e-08, 4.36713603438124e-08, 4.35367875261167e-08, 4.34026093977763e-08,
4.32688242740877e-08, 4.31354304451187e-08, 4.30024263322720e-08, 4.28698103009286e-08,
4.27375805871771e-08, 4.26057357782523e-08, 4.24742742963203e-08, 4.23431939844965e-08,
4.22124942789898e-08, 4.20821727084670e-08, 4.19522278426654e-08, 4.18226588811623e-08,
4.16934629063946e-08, 4.15646400655622e-08, 4.14361871363133e-08, 4.13081039822683e-08,
4.11803880430258e-08, 4.10530388163855e-08, 4.09260537661226e-08, 4.07994322150618e-08,
4.06731723027018e-08, 4.05472728223494e-08, 4.04217318015396e-08, 4.02965485668627e-08,
4.01717210120621e-08, 4.00472477994775e-08, 3.99231280593341e-08, 3.97993596139861e-08,
3.96759417187172e-08, 3.95528723135893e-08, 3.94301507241306e-08, 3.93077750468277e-08,
3.91857440222887e-08, 3.90640563759440e-08, 3.89427109159476e-08, 3.88217056906465e-08,
3.87010401505815e-08, 3.85807122279930e-08, 3.84607213064832e-08, 3.83410652580646e-08,
3.82217436631672e-08, 3.81027542218316e-08, 3.79840968945249e-08, 3.78657688102681e-08,
};

/*
 * Lookup tables for 0 < u <= 1/q.  u values are scaled so that the table
 * abscissas are integers from 0 to 511.
 */

static const double K0_v[] = {
0.00000000000000e+00, 8.55331880462993e-113, 3.65971714643556e-57, 1.39621540290836e-38,
2.84476908437209e-29, 1.12303710460486e-23, 6.14484059637914e-20, 2.90890513324591e-17,
2.97840420138948e-15, 1.09772432926736e-13, 1.97732632534651e-12, 2.11502766269012e-11,
1.52977710243462e-10, 8.18655900761893e-10, 3.45679060473624e-09, 1.20737971005356e-08,
3.61409284910936e-08, 9.52603986746437e-08, 2.25811404738288e-07, 4.89483614521397e-07,
9.83294779412664e-07, 1.85044592545374e-06, 3.29123592735941e-06, 5.57324542793471e-06,
9.04008924491929e-06, 1.41181937645746e-05, 2.13212459738358e-05, 3.12521533695935e-05,
4.46025271578136e-05, 6.21498420452039e-05, 8.47525293344794e-05, 1.13343326417020e-04,
1.48921236347743e-04, 1.92542473390067e-04, 2.45310715275504e-04, 3.08367014186600e-04,
3.82879626424720e-04, 4.70034009512565e-04, 5.71023180138921e-04, 6.87038588647104e-04,
8.19261624576100e-04, 9.68855833750115e-04, 1.13695989666243e-03, 1.32468139202676e-03,
1.53309134873445e-03, 1.76321957134436e-03, 2.01605071219933e-03, 2.29252105235647e-03,
2.59351594712074e-03, 2.91986788748716e-03, 3.27235512550267e-03, 3.65170081140509e-03,
4.05857259035913e-03, 4.49358260763737e-03, 4.95728787372462e-03, 5.45019094289608e-03,
5.97274086180615e-03, 6.52533434807917e-03, 7.10831716145964e-03, 7.72198563407403e-03,
8.36658832887980e-03, 9.04232779884761e-03, 9.74936242214016e-03, 1.04878082914390e-02,
1.12577411380837e-02, 1.20591982741177e-02, 1.28921805374726e-02, 1.37566542276816e-02,
1.46525530211880e-02, 1.55797798570706e-02, 1.65382087854644e-02, 1.75276867723331e-02,
1.85480354553396e-02, 1.95990528467559e-02, 2.06805149801598e-02, 2.17921774985791e-02,
2.29337771823611e-02, 2.41050334157779e-02, 2.53056495918273e-02, 2.65353144551895e-02,
2.77937033836743e-02, 2.90804796088518e-02, 3.03952953768118e-02, 3.17377930502523e-02,
3.31076061532471e-02, 3.45043603602539e-02, 3.59276744309780e-02, 3.73771610928534e-02,
3.88524278729393e-02, 4.03530778810666e-02, 4.18787105461388e-02, 4.34289223074418e-02,
4.50033072628752e-02, 4.66014577759601e-02, 4.82229650434652e-02, 4.98674196254874e-02,
5.15344119397434e-02, 5.32235327218162e-02, 5.49343734530457e-02, 5.66665267576965e-02,
5.84195867709872e-02, 6.01931494795110e-02, 6.19868130355234e-02, 6.38001780465115e-02,
6.56328478414060e-02, 6.74844287147433e-02, 6.93545301500264e-02, 7.12427650234722e-02,
7.31487497892975e-02, 7.50721046476248e-02, 7.70124536960377e-02, 7.89694250657911e-02,
8.09426510435968e-02, 8.29317681798834e-02, 8.49364173843802e-02, 8.69562440098242e-02,
8.89908979245527e-02, 9.10400335747043e-02, 9.31033100367115e-02, 9.51803910607287e-02,
9.72709451056105e-02, 9.93746453660159e-02, 1.01491169792186e-01, 1.03620201102906e-01,
1.05761426792143e-01, 1.07914539129813e-01, 1.10079235157115e-01, 1.12255216676832e-01,
1.14442190238986e-01, 1.16639867122211e-01, 1.18847963311176e-01, 1.21066199470379e-01,
1.23294300914619e-01, 1.25531997576419e-01, 1.27779023970663e-01, 1.30035119156708e-01,
1.32300026698185e-01, 1.34573494620727e-01, 1.36855275367809e-01, 1.39145125754908e-01,
1.41442806922151e-01, 1.43748084285619e-01, 1.46060727487475e-01, 1.48380510345046e-01,
1.50707210799006e-01, 1.53040610860786e-01, 1.55380496559326e-01, 1.57726657887283e-01,
1.60078888746795e-01, 1.62436986894904e-01, 1.64800753888711e-01, 1.67169995030366e-01,
1.69544519311955e-01, 1.71924139360357e-01, 1.74308671382143e-01, 1.76697935108569e-01,
1.79091753740729e-01, 1.81489953894906e-01, 1.83892365548181e-01, 1.86298821984342e-01,
1.88709159740116e-01, 1.91123218551792e-01, 1.93540841302234e-01, 1.95961873968341e-01,
1.98386165568965e-01, 2.00813568113321e-01, 2.03243936549906e-01, 2.05677128715946e-01,
2.08113005287406e-01, 2.10551429729542e-01, 2.12992268248058e-01, 2.15435389740831e-01,
2.17880665750255e-01, 2.20327970416189e-01, 2.22777180429526e-01, 2.25228174986384e-01,
2.27680835742938e-01, 2.30135046770872e-01, 2.32590694513483e-01, 2.35047667742417e-01,
2.37505857515050e-01, 2.39965157132506e-01, 2.42425462098326e-01, 2.44886670077762e-01,
2.47348680857727e-01, 2.49811396307362e-01, 2.52274720339255e-01, 2.54738558871270e-01,
2.57202819789020e-01, 2.59667412908944e-01, 2.62132249942011e-01, 2.64597244458034e-01,
2.67062311850584e-01, 2.69527369302507e-01, 2.71992335752036e-01, 2.74457131859487e-01,
2.76921679974540e-01, 2.79385904104091e-01, 2.81849729880671e-01, 2.84313084531429e-01,
2.86775896847664e-01, 2.89238097154906e-01, 2.91699617283537e-01, 2.94160390539936e-01,
2.96620351678161e-01, 2.99079436872133e-01, 3.01537583688340e-01, 3.03994731059036e-01,
3.06450819255938e-01, 3.08905789864408e-01, 3.11359585758110e-01, 3.13812151074147e-01,
3.16263431188651e-01, 3.18713372692841e-01, 3.21161923369516e-01, 3.23609032170007e-01,
3.26054649191541e-01, 3.28498725655057e-01, 3.30941213883418e-01, 3.33382067280052e-01,
3.35821240307992e-01, 3.38258688469313e-01, 3.40694368284960e-01, 3.43128237274967e-01,
3.45560253939047e-01, 3.47990377737553e-01, 3.50418569072806e-01, 3.52844789270782e-01,
3.55269000563141e-01, 3.57691166069617e-01, 3.60111249780729e-01, 3.62529216540834e-01,
3.64945032031507e-01, 3.67358662755235e-01, 3.69770076019429e-01, 3.72179239920744e-01,
3.74586123329700e-01, 3.76990695875603e-01, 3.79392927931749e-01, 3.81792790600927e-01,
3.84190255701188e-01, 3.86585295751900e-01, 3.88977883960065e-01, 3.91367994206905e-01,
3.93755601034705e-01, 3.96140679633914e-01, 3.98523205830490e-01, 4.00903156073494e-01,
4.03280507422924e-01, 4.05655237537780e-01, 4.08027324664365e-01, 4.10396747624813e-01,
4.12763485805830e-01, 4.15127519147665e-01, 4.17488828133284e-01, 4.19847393777761e-01,
4.22203197617868e-01, 4.24556221701870e-01, 4.26906448579517e-01, 4.29253861292227e-01,
4.31598443363461e-01, 4.33940178789283e-01, 4.36279052029101e-01, 4.38615047996590e-01,
4.40948152050786e-01, 4.43278349987355e-01, 4.45605628030028e-01, 4.47929972822204e-01,
4.50251371418709e-01, 4.52569811277723e-01, 4.54885280252851e-01, 4.57197766585358e-01,
4.59507258896543e-01, 4.61813746180270e-01, 4.64117217795630e-01, 4.66417663459755e-01,
4.68715073240767e-01, 4.71009437550858e-01, 4.73300747139506e-01, 4.75588993086823e-01,
4.77874166797025e-01, 4.80156259992035e-01, 4.82435264705199e-01, 4.84711173275128e-01,
4.86983978339658e-01, 4.89253672829923e-01, 4.91520249964543e-01, 4.93783703243920e-01,
4.96044026444648e-01, 4.98301213614023e-01, 5.00555259064665e-01, 5.02806157369235e-01,
5.05053903355259e-01, 5.07298492100044e-01, 5.09539918925699e-01, 5.11778179394241e-01,
5.14013269302801e-01, 5.16245184678922e-01, 5.18473921775935e-01, 5.20699477068438e-01,
5.22921847247851e-01, 5.25141029218054e-01, 5.27357020091120e-01, 5.29569817183107e-01,
5.31779418009955e-01, 5.33985820283437e-01, 5.36189021907208e-01, 5.38389020972907e-01,
5.40585815756353e-01, 5.42779404713797e-01, 5.44969786478253e-01, 5.47156959855895e-01,
5.49340923822525e-01, 5.51521677520102e-01, 5.53699220253343e-01, 5.55873551486382e-01,
5.58044670839493e-01, 5.60212578085879e-01, 5.62377273148516e-01, 5.64538756097057e-01,
5.66697027144800e-01, 5.68852086645700e-01, 5.71003935091452e-01, 5.73152573108620e-01,
5.75298001455819e-01, 5.77440221020953e-01, 5.79579232818506e-01, 5.81715037986877e-01,
5.83847637785775e-01, 5.85977033593649e-01, 5.88103226905182e-01, 5.90226219328816e-01,
5.92346012584337e-01, 5.94462608500494e-01, 5.96576009012668e-01, 5.98686216160587e-01,
6.00793232086074e-01, 6.02897059030849e-01, 6.04997699334360e-01, 6.07095155431665e-01,
6.09189429851347e-01, 6.11280525213467e-01, 6.13368444227561e-01, 6.15453189690669e-01,
6.17534764485402e-01, 6.19613171578045e-01, 6.21688414016695e-01, 6.23760494929436e-01,
6.25829417522544e-01, 6.27895185078726e-01, 6.29957800955395e-01, 6.32017268582976e-01,
6.34073591463236e-01, 6.36126773167658e-01, 6.38176817335834e-01, 6.40223727673893e-01,
6.42267507952960e-01, 6.44308162007636e-01, 6.46345693734512e-01, 6.48380107090713e-01,
6.50411406092463e-01, 6.52439594813676e-01, 6.54464677384582e-01, 6.56486657990368e-01,
6.58505540869850e-01, 6.60521330314168e-01, 6.62534030665508e-01, 6.64543646315841e-01,
6.66550181705691e-01, 6.68553641322927e-01, 6.70554029701572e-01, 6.72551351420635e-01,
6.74545611102972e-01, 6.76536813414156e-01, 6.78524963061380e-01, 6.80510064792372e-01,
6.82492123394334e-01, 6.84471143692897e-01, 6.86447130551102e-01, 6.88420088868394e-01,
6.90390023579635e-01, 6.92356939654141e-01, 6.94320842094728e-01, 6.96281735936785e-01,
6.98239626247354e-01, 7.00194518124241e-01, 7.02146416695129e-01, 7.04095327116714e-01,
7.06041254573862e-01, 7.07984204278771e-01, 7.09924181470158e-01, 7.11861191412457e-01,
7.13795239395029e-01, 7.15726330731397e-01, 7.17654470758481e-01, 7.19579664835858e-01,
7.21501918345036e-01, 7.23421236688732e-01, 7.25337625290174e-01, 7.27251089592409e-01,
7.29161635057629e-01, 7.31069267166507e-01, 7.32973991417546e-01, 7.34875813326437e-01,
7.36774738425437e-01, 7.38670772262750e-01, 7.40563920401926e-01, 7.42454188421267e-01,
7.44341581913250e-01, 7.46226106483949e-01, 7.48107767752487e-01, 7.49986571350476e-01,
7.51862522921487e-01, 7.53735628120519e-01, 7.55605892613480e-01, 7.57473322076683e-01,
7.59337922196341e-01, 7.61199698668084e-01, 7.63058657196478e-01, 7.64914803494552e-01,
7.66768143283340e-01, 7.68618682291426e-01, 7.70466426254501e-01, 7.72311380914927e-01,
7.74153552021314e-01, 7.75992945328093e-01, 7.77829566595114e-01, 7.79663421587238e-01,
7.81494516073944e-01, 7.83322855828942e-01, 7.85148446629791e-01, 7.86971294257531e-01,
7.88791404496312e-01, 7.90608783133043e-01, 7.92423435957034e-01, 7.94235368759657e-01,
7.96044587334007e-01, 7.97851097474573e-01, 7.99654904976909e-01, 8.01456015637323e-01,
8.03254435252559e-01, 8.05050169619498e-01, 8.06843224534854e-01, 8.08633605794884e-01,
8.10421319195097e-01, 8.12206370529978e-01, 8.13988765592707e-01, 8.15768510174891e-01,
8.17545610066299e-01, 8.19320071054601e-01, 8.21091898925118e-01, 8.22861099460567e-01,
8.24627678440820e-01, 8.26391641642667e-01, 8.28152994839579e-01, 8.29911743801480e-01,
8.31667894294522e-01, 8.33421452080864e-01, 8.35172422918462e-01, 8.36920812560849e-01,
8.38666626756939e-01, 8.40409871250818e-01, 8.42150551781547e-01, 8.43888674082971e-01,
8.45624243883529e-01, 8.47357266906066e-01, 8.49087748867654e-01, 8.50815695479415e-01,
8.52541112446345e-01, 8.54264005467144e-01, 8.55984380234053e-01, 8.57702242432688e-01,
8.59417597741882e-01, 8.61130451833532e-01, 8.62840810372441e-01, 8.64548679016175e-01,
8.66254063414915e-01, 8.67956969211315e-01, 8.69657402040365e-01, 8.71355367529251e-01,
8.73050871297228e-01, 8.74743918955483e-01, 8.76434516107018e-01, 8.78122668346517e-01,
8.79808381260231e-01, 8.81491660425858e-01, 8.83172511412428e-01, 8.84850939780190e-01,
8.86526951080504e-01, 8.88200550855732e-01, 8.89871744639134e-01, 8.91540537954767e-01,
8.93206936317383e-01, 8.94870945232335e-01, 8.96532570195482e-01, 8.98191816693094e-01,
8.99848690201764e-01, 9.01503196188321e-01, 9.03155340109744e-01, 9.04805127413080e-01,
9.06452563535358e-01, 9.08097653903518e-01, 9.09740403934328e-01, 9.11380819034313e-01,
9.13018904599679e-01, 9.14654666016245e-01, 9.16288108659373e-01, 9.17919237893902e-01,
9.19548059074084e-01, 9.21174577543516e-01, 9.22798798635085e-01, 9.24420727670904e-01,
};

static const double K0_v2[] = {
0.00000000000000e+00, -3.21673333280220e-21, 1.12585666648077e-20, -4.18175333264287e-20,
1.56011566669354e-19, -5.82217503036840e-19, 2.23428439072815e-18, 2.06112456910268e-17,
2.83560827997569e-15, 9.24816692096960e-14, 1.38799757857567e-12, 1.16609244256225e-11,
6.46227880339402e-11, 2.63698680340486e-10, 8.53039004060033e-10, 2.30301709524444e-09,
5.38501750972080e-09, 1.12092516588644e-08, 2.12095117349157e-08, 3.70739051209369e-08,
6.06338228894958e-08, 9.37307844708913e-08, 1.38081895091531e-07, 1.95161133832600e-07,
2.66107885987359e-07, 3.51668024888738e-07, 4.52167704063528e-07, 5.67516345353593e-07,
6.97233306984600e-07, 8.40491525878100e-07, 9.96172991388326e-07, 1.16292630183429e-06,
1.33923464945571e-06, 1.52346221194425e-06, 1.71392134588031e-06, 1.90890943019363e-06,
2.10675426036916e-06, 2.30584437805476e-06, 2.50465576592262e-06, 2.70177044008138e-06,
2.89588989456576e-06, 3.08584322667322e-06, 3.27059093704347e-06, 3.44922547717105e-06,
3.62096849762260e-06, 3.78516643456627e-06, 3.94128400916811e-06, 4.08889683093910e-06,
4.22768327419064e-06, 4.35741567445596e-06, 4.47795167708536e-06, 4.58922550410142e-06,
4.69123935812738e-06, 4.78405538759711e-06, 4.86778790048407e-06, 4.94259609468714e-06,
5.00867745937271e-06, 5.06626143076898e-06, 5.11560392500578e-06, 5.15698210312089e-06,
5.19068985389553e-06, 5.21703364333848e-06, 5.23632889749642e-06, 5.24889677298864e-06,
5.25506135638246e-06, 5.25514719079415e-06, 5.24947720131278e-06, 5.23837085805347e-06,
5.22214266389934e-06, 5.20110086249746e-06, 5.17554639739861e-06, 5.14577202273549e-06,
5.11206164949655e-06, 5.07468978902340e-06, 5.03392118206271e-06, 4.99001049815257e-06,
4.94320218798874e-06, 4.89373038470870e-06, 4.84181890572099e-06, 4.78768130522536e-06,
4.73152099600439e-06, 4.67353140347384e-06, 4.61389617263497e-06, 4.55278938643544e-06,
4.49037583591814e-06, 4.42681128181167e-06, 4.36224275425456e-06, 4.29680885242786e-06,
4.23064004649926e-06, 4.16385900306738e-06, 4.09658088611143e-06, 4.02891368323619e-06,
3.96095851132453e-06, 3.89280992298287e-06, 3.82455621696684e-06, 3.75627972627275e-06,
3.68805711176736e-06, 3.61995964335608e-06, 3.55205347152321e-06, 3.48439989194030e-06,
3.41705560053015e-06, 3.35007293911428e-06, 3.28350013157325e-06, 3.21738151023017e-06,
3.15175773395744e-06, 3.08666599681368e-06, 3.02214022450798e-06, 2.95821126790008e-06,
2.89490708329560e-06, 2.83225290100947e-06, 2.77027139820342e-06, 2.70898284677766e-06,
2.64840526687118e-06, 2.58855456671994e-06, 2.52944467643521e-06, 2.47108767468257e-06,
2.41349390932868e-06, 2.35667211122178e-06, 2.30062950130727e-06, 2.24537189347998e-06,
2.19090378945772e-06, 2.13722847225199e-06, 2.08434808695808e-06, 2.03226372906727e-06,
1.98097551341457e-06, 1.93048265093105e-06, 1.88078351472227e-06, 1.83187570451115e-06,
1.78375610512098e-06, 1.73642094595331e-06, 1.68986585053878e-06, 1.64408589000984e-06,
1.59907562703813e-06, 1.55482916133693e-06, 1.51134017177735e-06, 1.46860195212417e-06,
1.42660745182328e-06, 1.38534930536430e-06, 1.34481986749880e-06, 1.30501124170703e-06,
1.26591530849875e-06, 1.22752375033199e-06, 1.18982807812484e-06, 1.15281965189048e-06,
1.11648970338541e-06, 1.08082935461107e-06, 1.04582963784358e-06, 1.01148151083883e-06,
9.77775874625630e-07, 9.44703586798358e-07, 9.12255476428817e-07, 8.80422355975138e-07,
8.49195033396718e-07, 8.18564323422726e-07, 7.88521056698949e-07, 7.59056090412917e-07,
7.30160315238567e-07, 7.01824665227175e-07, 6.74040122952077e-07, 6.46797727563600e-07,
6.20088580723311e-07, 5.93903851116388e-07, 5.68234781110036e-07, 5.43072689552532e-07,
5.18408977732893e-07, 4.94235131331423e-07, 4.70542725004284e-07, 4.47323425270565e-07,
4.24568992337305e-07, 4.02271283179482e-07, 3.80422253604300e-07, 3.59013959598353e-07,
3.38038559145032e-07, 3.17488313794043e-07, 2.97355588420748e-07, 2.77632854560572e-07,
2.58312688275494e-07, 2.39387772772403e-07, 2.20850897640460e-07, 2.02694959671864e-07,
1.84912962117787e-07, 1.67498015761401e-07, 1.50443337618040e-07, 1.33742251064711e-07,
1.17388185872505e-07, 1.01374676781689e-07, 8.56953638121092e-08, 7.03439910864743e-08,
5.53144059532347e-08, 4.06005589811115e-08, 2.61965020825362e-08, 1.20963884203349e-08,
-1.70552917271714e-09, -1.52148987176915e-08, -2.84372702988597e-08, -4.13780974748443e-08,
-5.40427376411101e-08, -6.64364542203643e-08, -7.85644164757604e-08, -9.04317021755062e-08,
-1.02043297723858e-07, -1.13404099524451e-07, -1.24518915945505e-07, -1.35392467477041e-07,
-1.46029388855272e-07, -1.56434229900226e-07, -1.66611456868728e-07, -1.76565453532331e-07,
-1.86300522840076e-07, -1.95820887849262e-07, -2.05130693000944e-07, -2.14234005636687e-07,
-2.23134816649662e-07, -2.31837042691767e-07, -2.40344526241979e-07, -2.48661038066313e-07,
-2.56790277024086e-07, -2.64735872879299e-07, -2.72501386018018e-07, -2.80090309542219e-07,
-2.87506070225343e-07, -2.94752029479624e-07, -3.01831484859485e-07, -3.08747670741166e-07,
-3.15503759762953e-07, -3.22102864211717e-07, -3.28548036086426e-07, -3.34842269565391e-07,
-3.40988501010275e-07, -3.46989610257564e-07, -3.52848422276541e-07, -3.58567707017477e-07,
-3.64150181747089e-07, -3.69598511073350e-07, -3.74915308063524e-07, -3.80103135686890e-07,
-3.85164507586360e-07, -3.90101888212217e-07, -3.94917695345821e-07, -3.99614299085883e-07,
-4.04194024711951e-07, -4.08659151625555e-07, -4.13011915887896e-07, -4.17254509898687e-07,
-4.21389083807655e-07, -4.25417746129364e-07, -4.29342564701914e-07, -4.33165567011263e-07,
-4.36888741876539e-07, -4.40514039212339e-07, -4.44043371348134e-07, -4.47478613483965e-07,
-4.50821604989125e-07, -4.54074149080822e-07, -4.57238014365155e-07, -4.60314935655877e-07,
-4.63306613266195e-07, -4.66214715799977e-07, -4.69040878743420e-07, -4.71786706307982e-07,
-4.74453771961796e-07, -4.77043618180312e-07, -4.79557758633179e-07, -4.81997676624957e-07,
-4.84364827757616e-07, -4.86660639277511e-07, -4.88886510857672e-07, -4.91043815174753e-07,
-4.93133898704757e-07, -4.95158081793430e-07, -4.97117659410843e-07, -4.99013901837430e-07,
-5.00848054440402e-07, -5.02621339436372e-07, -5.04334954782089e-07, -5.05990075738652e-07,
-5.07587855497073e-07, -5.09129423998410e-07, -5.10615890972943e-07, -5.12048343456548e-07,
-5.13427848966779e-07, -5.14755453442307e-07, -5.16032183700053e-07, -5.17259046439580e-07,
-5.18437029379816e-07, -5.19567101038433e-07, -5.20650211920906e-07, -5.21687293926184e-07,
-5.22679261701484e-07, -5.23627011758732e-07, -5.24531424431962e-07, -5.25393362371373e-07,
-5.26213672611298e-07, -5.26993185521924e-07, -5.27732715935241e-07, -5.28433063464280e-07,
-5.29095011543498e-07, -5.29719330503931e-07, -5.30306774003739e-07, -5.30858083125448e-07,
-5.31373984103558e-07, -5.31855189098032e-07, -5.32302398148274e-07, -5.32716296245869e-07,
-5.33097556983421e-07, -5.33446840323364e-07, -5.33764794099110e-07, -5.34052054016411e-07,
-5.34309243479018e-07, -5.34536974395730e-07, -5.34735847124117e-07, -5.34906450554727e-07,
-5.35049362829732e-07, -5.35165150604575e-07, -5.35254370838662e-07, -5.35317568922855e-07,
-5.35355280937104e-07, -5.35368032265608e-07, -5.35356339102167e-07, -5.35320706811216e-07,
-5.35261632868925e-07, -5.35179603954202e-07, -5.35075098759395e-07, -5.34948585873749e-07,
-5.34800526663302e-07, -5.34631372085101e-07, -5.34441566333189e-07, -5.34231543878135e-07,
-5.34001732222843e-07, -5.33752550168048e-07, -5.33484408996920e-07, -5.33197712135695e-07,
-5.32892855881654e-07, -5.32570228606933e-07, -5.32230211772012e-07, -5.31873179998626e-07,
-5.31499499875640e-07, -5.31109532997323e-07, -5.30703631887743e-07, -5.30282145049265e-07,
-5.29845411946403e-07, -5.29393768251948e-07, -5.28927541091851e-07, -5.28447053382673e-07,
-5.27952620784816e-07, -5.27444553778989e-07, -5.26923156625970e-07, -5.26388728562905e-07,
-5.25841562611854e-07, -5.25281946595822e-07, -5.24710163263663e-07, -5.24126489662628e-07,
-5.23531198302014e-07, -5.22924555679539e-07, -5.22306824680728e-07, -5.21678261895077e-07,
-5.21039120511927e-07, -5.20389647749069e-07, -5.19730087357469e-07, -5.19060677724888e-07,
-5.18381653625992e-07, -5.17693244226929e-07, -5.16995676430327e-07, -5.16289170596154e-07,
-5.15573944987396e-07, -5.14850212702596e-07, -5.14118183060729e-07, -5.13378062015719e-07,
-5.12630051111924e-07, -5.11874348028016e-07, -5.11111148110522e-07, -5.10340641026437e-07,
-5.09563014625637e-07, -5.08778452608568e-07, -5.07987134997079e-07, -5.07189239249530e-07,
-5.06384938771221e-07, -5.05574404093836e-07, -5.04757802755861e-07, -5.03935298490429e-07,
-5.03107053261285e-07, -5.02273224371948e-07, -5.01433967775859e-07, -5.00589435498187e-07,
-4.99739776865296e-07, -4.98885139273697e-07, -4.98025665994201e-07, -4.97161498857276e-07,
-4.96292776257783e-07, -4.95419634564904e-07, -4.94542207253235e-07, -4.93660625303172e-07,
-4.92775017467458e-07, -4.91885509914837e-07, -4.90992226722761e-07, -4.90095289151079e-07,
-4.89194816611295e-07, -4.88290926180373e-07, -4.87383732910127e-07, -4.86473348964835e-07,
-4.85559885651171e-07, -4.84643450601750e-07, -4.83724151459907e-07, -4.82802091395530e-07,
-4.81877374142097e-07, -4.80950099101852e-07, -4.80020366118108e-07, -4.79088270939796e-07,
-4.78153909376124e-07, -4.77217374095166e-07, -4.76278756724528e-07, -4.75338147090998e-07,
-4.74395632940032e-07, -4.73451300596908e-07, -4.72505234934102e-07, -4.71557518840616e-07,
-4.70608233934021e-07, -4.69657460019294e-07, -4.68705275542231e-07, -4.67751757427198e-07,
-4.66796981161661e-07, -4.65841020287273e-07, -4.64883948239966e-07, -4.63925835051215e-07,
-4.62966751708464e-07, -4.62006765560101e-07, -4.61045944343117e-07, -4.60084353771317e-07,
-4.59122058380868e-07, -4.58159121226018e-07, -4.57195604805790e-07, -4.56231569659894e-07,
-4.55267075061578e-07, -4.54302180536886e-07, -4.53336942425445e-07, -4.52371417458333e-07,
-4.51405660434520e-07, -4.50439725718395e-07, -4.49473666015715e-07, -4.48507533107736e-07,
-4.47541378470211e-07, -4.46575250840428e-07, -4.45609200556100e-07, -4.44643273958631e-07,
-4.43677519339742e-07, -4.42711981519260e-07, -4.41746706374089e-07, -4.40781737803472e-07,
-4.39817118788657e-07, -4.38852892076348e-07, -4.37889098938762e-07, -4.36925780230276e-07,
-4.35962975510237e-07, -4.35000723829718e-07, -4.34039063904180e-07, -4.33078032191983e-07,
-4.32117666410878e-07, -4.31158001387126e-07, -4.30199073149732e-07, -4.29240915586170e-07,
-4.28283562286755e-07, -4.27327046730273e-07, -4.26371400474252e-07, -4.25416655767359e-07,
-4.24462843126779e-07, -4.23509992643152e-07, -4.22558134514102e-07, -4.21607297048495e-07,
-4.20657508897807e-07, -4.19708797677529e-07, -4.18761190474607e-07, -4.17814714084461e-07,
-4.16869393888535e-07, -4.15925255553564e-07, -4.14982324130925e-07, -4.14040623073370e-07,
-4.13100177181370e-07, -4.12161008240309e-07, -4.11223140310494e-07, -4.10286594254220e-07,
-4.09351392569115e-07, -4.08417555963800e-07, -4.07485104783405e-07, -4.06554060173552e-07,
-4.05624440108307e-07, -4.04696265787732e-07, -4.03769554230583e-07, -4.02844324741582e-07,
-4.01920594882543e-07, -4.00998382015969e-07, -4.00077703046905e-07, -3.99158575022166e-07,
-3.98241013546675e-07, -3.97325034522082e-07, -3.96410653882976e-07, -3.95497885470131e-07,
-3.94586745360418e-07, -3.93677246221818e-07, -3.92769403239999e-07, -3.91863229046586e-07,
-3.90958737310361e-07, -3.90055940327563e-07, -3.89154851072683e-07, -3.88255481179755e-07,
-3.87357842858557e-07, -3.86461947356353e-07, -3.85567805530974e-07, -3.84675428873131e-07,
-3.83784827286550e-07, -3.82896011282995e-07, -3.82008990751105e-07, -3.81123775243533e-07,
};

double am_K0(double x)
{
    unsigned int i, ip;
    double a, b, c, d;
    double u;

    if (x < 0.5) {
        u = -log(x);
        x *= K0_XSCALE;
        i = (unsigned int)(x);
        ip = i + 1;
        a = (double)ip - x;
        b = 1. - a;
        c = a * a * a - a;
        d = b * b * b - b;
        return u + a * K0_y[i] + b * K0_y[ip] + c * K0_y2[i] + d * K0_y2[ip];
    }
    u = K0_USCALE / x;
    i = (unsigned int)(u);
    ip = i + 1;
    a = (double)ip - u;
    b = 1. - a;
    c = a * a * a - a;
    d = b * b * b - b;
    return a * K0_v[i] + b * K0_v[ip] + c * K0_v2[i] + d * K0_v2[ip];
}   /* am_K0() */


/***********************************************************
* double am_xK1(double x)
*
* Purpose:
*   Computes x * K1(x), where K1(x) is a modified Bessel function,
*   over the range 0 < x < inf.  To save time, no argument checking
*   is done.
*
*   For 0 < x < q, where q = 0.5, the function is approximated by
*
*       x * K1(x) = y(x),
*
*   where y(x) is computed by cubic spline interpolation of a lookup
*   table.  For x >= q, the function is approximated by
*
*       x * K1(x) = v(u),
*
*   where u = 1/x, and v(u) is again computed by cubic spline
*   interpolation of a lookup table.
*
*   The lookup tables were computed using Mathcad 7's implementation
*   of K1(), then the accuracy of the interpolation was evaluated on
*   a finer mesh.  For x < q, the worst-case _normalized_ error is
*   about 8e-9, at x = 2e-4, where x * K1(x) = 1.0.  For x > q, the
*   worst-case _absolute_ error is about -8e-11, at x = 11.5, where
*   x * K1(x) = 4.4e-5 (i.e. a normalized error of about -2e-6.)
*
* Arguments:
*   double x
*
* Return:
*   K0(x)
************************************************************/

/*
 * The lookup tables below all have n = 1024 points.  Note that the
 * table for x > q was computed starting at x = q - 1.e-6, to
 * place the point x = q inside the interpolation table.
 */

#define XK1_XSCALE  2046.0              /* (n - 1) / q */
#define XK1_USCALE  511.498977000000    /* (n - 1) / (1 / (q + 1.e-6)) */

/*
 * Lookup tables for 0 < x < q.  x values are scaled so that the table
 * abscissas are integers from 0 to 511.
 */

static const double XK1_y[] = {
1.00000000000000e+00, 9.99999015845030e-01, 9.99996394544598e-01, 9.99992323591887e-01,
9.99986902832633e-01, 9.99980201990762e-01, 9.99972274826796e-01, 9.99963165138359e-01,
9.99952909894508e-01, 9.99941541086009e-01, 9.99929086910910e-01, 9.99915572580558e-01,
9.99901020892802e-01, 9.99885452654329e-01, 9.99868887000881e-01, 9.99851341645871e-01,
9.99832833077278e-01, 9.99813376716260e-01, 9.99792987046811e-01, 9.99771677723110e-01,
9.99749461659407e-01, 9.99726351106040e-01, 9.99702357714302e-01, 9.99677492592233e-01,
9.99651766352961e-01, 9.99625189156854e-01, 9.99597770748512e-01, 9.99569520489386e-01,
9.99540447386716e-01, 9.99510560119288e-01, 9.99479867060497e-01, 9.99448376299045e-01,
9.99416095657614e-01, 9.99383032709747e-01, 9.99349194795181e-01, 9.99314589033794e-01,
9.99279222338350e-01, 9.99243101426160e-01, 9.99206232829781e-01, 9.99168622906865e-01,
9.99130277849236e-01, 9.99091203691281e-01, 9.99051406317712e-01, 9.99010891470779e-01,
9.98969664756956e-01, 9.98927731653184e-01, 9.98885097512682e-01, 9.98841767570377e-01,
9.98797746947983e-01, 9.98753040658763e-01, 9.98707653611993e-01, 9.98661590617154e-01,
9.98614856387879e-01, 9.98567455545667e-01, 9.98519392623387e-01, 9.98470672068583e-01,
9.98421298246599e-01, 9.98371275443534e-01, 9.98320607869041e-01, 9.98269299658980e-01,
9.98217354877933e-01, 9.98164777521595e-01, 9.98111571519046e-01, 9.98057740734907e-01,
9.98003288971403e-01, 9.97948219970319e-01, 9.97892537414866e-01, 9.97836244931469e-01,
9.97779346091468e-01, 9.97721844412743e-01, 9.97663743361270e-01, 9.97605046352610e-01,
9.97545756753336e-01, 9.97485877882395e-01, 9.97425413012420e-01, 9.97364365370981e-01,
9.97302738141798e-01, 9.97240534465888e-01, 9.97177757442685e-01, 9.97114410131106e-01,
9.97050495550575e-01, 9.96986016682019e-01, 9.96920976468816e-01, 9.96855377817714e-01,
9.96789223599713e-01, 9.96722516650918e-01, 9.96655259773363e-01, 9.96587455735801e-01,
9.96519107274473e-01, 9.96450217093844e-01, 9.96380787867320e-01, 9.96310822237936e-01,
9.96240322819026e-01, 9.96169292194868e-01, 9.96097732921307e-01, 9.96025647526364e-01,
9.95953038510816e-01, 9.95879908348768e-01, 9.95806259488198e-01, 9.95732094351496e-01,
9.95657415335973e-01, 9.95582224814369e-01, 9.95506525135332e-01, 9.95430318623898e-01,
9.95353607581940e-01, 9.95276394288618e-01, 9.95198681000810e-01, 9.95120469953531e-01,
9.95041763360342e-01, 9.94962563413742e-01, 9.94882872285560e-01, 9.94802692127325e-01,
9.94722025070635e-01, 9.94640873227504e-01, 9.94559238690720e-01, 9.94477123534167e-01,
9.94394529813165e-01, 9.94311459564782e-01, 9.94227914808147e-01, 9.94143897544752e-01,
9.94059409758749e-01, 9.93974453417235e-01, 9.93889030470538e-01, 9.93803142852484e-01,
9.93716792480668e-01, 9.93629981256717e-01, 9.93542711066538e-01, 9.93454983780571e-01,
9.93366801254031e-01, 9.93278165327144e-01, 9.93189077825376e-01, 9.93099540559664e-01,
9.93009555326631e-01, 9.92919123908806e-01, 9.92828248074833e-01, 9.92736929579676e-01,
9.92645170164822e-01, 9.92552971558480e-01, 9.92460335475767e-01, 9.92367263618904e-01,
9.92273757677396e-01, 9.92179819328215e-01, 9.92085450235974e-01, 9.91990652053102e-01,
9.91895426420011e-01, 9.91799774965265e-01, 9.91703699305739e-01, 9.91607201046781e-01,
9.91510281782365e-01, 9.91412943095245e-01, 9.91315186557103e-01, 9.91217013728699e-01,
9.91118426160010e-01, 9.91019425390374e-01, 9.90920012948626e-01, 9.90820190353235e-01,
9.90719959112436e-01, 9.90619320724359e-01, 9.90518276677158e-01, 9.90416828449135e-01,
9.90314977508864e-01, 9.90212725315313e-01, 9.90110073317957e-01, 9.90007022956899e-01,
9.89903575662982e-01, 9.89799732857904e-01, 9.89695495954320e-01, 9.89590866355959e-01,
9.89485845457724e-01, 9.89380434645800e-01, 9.89274635297750e-01, 9.89168448782623e-01,
9.89061876461048e-01, 9.88954919685332e-01, 9.88847579799554e-01, 9.88739858139662e-01,
9.88631756033559e-01, 9.88523274801202e-01, 9.88414415754682e-01, 9.88305180198316e-01,
9.88195569428734e-01, 9.88085584734959e-01, 9.87975227398496e-01, 9.87864498693408e-01,
9.87753399886399e-01, 9.87641932236894e-01, 9.87530096997115e-01, 9.87417895412159e-01,
9.87305328720072e-01, 9.87192398151923e-01, 9.87079104931879e-01, 9.86965450277273e-01,
9.86851435398680e-01, 9.86737061499982e-01, 9.86622329778438e-01, 9.86507241424750e-01,
9.86391797623135e-01, 9.86275999551381e-01, 9.86159848380921e-01, 9.86043345276888e-01,
9.85926491398185e-01, 9.85809287897541e-01, 9.85691735921573e-01, 9.85573836610847e-01,
9.85455591099937e-01, 9.85337000517479e-01, 9.85218065986234e-01, 9.85098788623140e-01,
9.84979169539369e-01, 9.84859209840380e-01, 9.84738910625977e-01, 9.84618272990358e-01,
9.84497298022168e-01, 9.84375986804553e-01, 9.84254340415208e-01, 9.84132359926429e-01,
9.84010046405162e-01, 9.83887400913051e-01, 9.83764424506489e-01, 9.83641118236660e-01,
9.83517483149591e-01, 9.83393520286198e-01, 9.83269230682327e-01, 9.83144615368803e-01,
9.83019675371474e-01, 9.82894411711252e-01, 9.82768825404160e-01, 9.82642917461371e-01,
9.82516688889253e-01, 9.82390140689409e-01, 9.82263273858717e-01, 9.82136089389373e-01,
9.82008588268929e-01, 9.81880771480331e-01, 9.81752640001964e-01, 9.81624194807680e-01,
9.81495436866848e-01, 9.81366367144380e-01, 9.81236986600777e-01, 9.81107296192161e-01,
9.80977296870309e-01, 9.80846989582696e-01, 9.80716375272520e-01, 9.80585454878747e-01,
9.80454229336137e-01, 9.80322699575283e-01, 9.80190866522642e-01, 9.80058731100568e-01,
9.79926294227346e-01, 9.79793556817223e-01, 9.79660519780442e-01, 9.79527184023270e-01,
9.79393550448032e-01, 9.79259619953138e-01, 9.79125393433120e-01, 9.78990871778656e-01,
9.78856055876600e-01, 9.78720946610016e-01, 9.78585544858202e-01, 9.78449851496721e-01,
9.78313867397429e-01, 9.78177593428502e-01, 9.78041030454466e-01, 9.77904179336222e-01,
9.77767040931073e-01, 9.77629616092752e-01, 9.77491905671449e-01, 9.77353910513836e-01,
9.77215631463090e-01, 9.77077069358927e-01, 9.76938225037616e-01, 9.76799099332014e-01,
9.76659693071583e-01, 9.76520007082422e-01, 9.76380042187282e-01, 9.76239799205600e-01,
9.76099278953515e-01, 9.75958482243893e-01, 9.75817409886354e-01, 9.75676062687289e-01,
9.75534441449889e-01, 9.75392546974162e-01, 9.75250380056957e-01, 9.75107941491987e-01,
9.74965232069851e-01, 9.74822252578052e-01, 9.74679003801022e-01, 9.74535486520143e-01,
9.74391701513764e-01, 9.74247649557225e-01, 9.74103331422878e-01, 9.73958747880103e-01,
9.73813899695333e-01, 9.73668787632071e-01, 9.73523412450908e-01, 9.73377774909547e-01,
9.73231875762818e-01, 9.73085715762699e-01, 9.72939295658334e-01, 9.72792616196052e-01,
9.72645678119386e-01, 9.72498482169089e-01, 9.72351029083154e-01, 9.72203319596833e-01,
9.72055354442651e-01, 9.71907134350429e-01, 9.71758660047293e-01, 9.71609932257701e-01,
9.71460951703453e-01, 9.71311719103709e-01, 9.71162235175010e-01, 9.71012500631289e-01,
9.70862516183890e-01, 9.70712282541584e-01, 9.70561800410586e-01, 9.70411070494568e-01,
9.70260093494679e-01, 9.70108870109556e-01, 9.69957401035343e-01, 9.69805686965704e-01,
9.69653728591842e-01, 9.69501526602508e-01, 9.69349081684020e-01, 9.69196394520279e-01,
9.69043465792780e-01, 9.68890296180626e-01, 9.68736886360549e-01, 9.68583237006916e-01,
9.68429348791749e-01, 9.68275222384734e-01, 9.68120858453239e-01, 9.67966257662329e-01,
9.67811420674772e-01, 9.67656348151061e-01, 9.67501040749422e-01, 9.67345499125830e-01,
9.67189723934020e-01, 9.67033715825501e-01, 9.66877475449570e-01, 9.66721003453323e-01,
9.66564300481670e-01, 9.66407367177343e-01, 9.66250204180913e-01, 9.66092812130802e-01,
9.65935191663291e-01, 9.65777343412538e-01, 9.65619268010586e-01, 9.65460966087375e-01,
9.65302438270756e-01, 9.65143685186501e-01, 9.64984707458316e-01, 9.64825505707851e-01,
9.64666080554711e-01, 9.64506432616471e-01, 9.64346562508682e-01, 9.64186470844887e-01,
9.64026158236628e-01, 9.63865625293460e-01, 9.63704872622960e-01, 9.63543900830739e-01,
9.63382710520450e-01, 9.63221302293803e-01, 9.63059676750573e-01, 9.62897834488609e-01,
9.62735776103848e-01, 9.62573502190320e-01, 9.62411013340165e-01, 9.62248310143636e-01,
9.62085393189115e-01, 9.61922263063119e-01, 9.61758920350312e-01, 9.61595365633512e-01,
9.61431599493706e-01, 9.61267622510051e-01, 9.61103435259895e-01, 9.60939038318775e-01,
9.60774432260434e-01, 9.60609617656827e-01, 9.60444595078133e-01, 9.60279365092759e-01,
9.60113928267355e-01, 9.59948285166820e-01, 9.59782436354308e-01, 9.59616382391246e-01,
9.59450123837333e-01, 9.59283661250553e-01, 9.59116995187185e-01, 9.58950126201807e-01,
9.58783054847312e-01, 9.58615781674909e-01, 9.58448307234135e-01, 9.58280632072862e-01,
9.58112756737308e-01, 9.57944681772042e-01, 9.57776407719993e-01, 9.57607935122460e-01,
9.57439264519119e-01, 9.57270396448027e-01, 9.57101331445638e-01, 9.56932070046803e-01,
9.56762612784784e-01, 9.56592960191256e-01, 9.56423112796319e-01, 9.56253071128505e-01,
9.56082835714784e-01, 9.55912407080571e-01, 9.55741785749738e-01, 9.55570972244615e-01,
9.55399967086002e-01, 9.55228770793176e-01, 9.55057383883894e-01, 9.54885806874405e-01,
9.54714040279457e-01, 9.54542084612301e-01, 9.54369940384698e-01, 9.54197608106931e-01,
9.54025088287806e-01, 9.53852381434663e-01, 9.53679488053379e-01, 9.53506408648379e-01,
9.53333143722640e-01, 9.53159693777701e-01, 9.52986059313662e-01, 9.52812240829200e-01,
9.52638238821571e-01, 9.52464053786615e-01, 9.52289686218766e-01, 9.52115136611055e-01,
9.51940405455120e-01, 9.51765493241209e-01, 9.51590400458189e-01, 9.51415127593550e-01,
9.51239675133412e-01, 9.51064043562534e-01, 9.50888233364315e-01, 9.50712245020802e-01,
9.50536079012698e-01, 9.50359735819368e-01, 9.50183215918840e-01, 9.50006519787818e-01,
9.49829647901683e-01, 9.49652600734499e-01, 9.49475378759023e-01, 9.49297982446704e-01,
9.49120412267697e-01, 9.48942668690860e-01, 9.48764752183766e-01, 9.48586663212706e-01,
9.48408402242696e-01, 9.48229969737481e-01, 9.48051366159539e-01, 9.47872591970092e-01,
9.47693647629107e-01, 9.47514533595300e-01, 9.47335250326147e-01, 9.47155798277884e-01,
9.46976177905515e-01, 9.46796389662816e-01, 9.46616434002342e-01, 9.46436311375430e-01,
9.46256022232207e-01, 9.46075567021590e-01, 9.45894946191297e-01, 9.45714160187849e-01,
9.45533209456574e-01, 9.45352094441616e-01, 9.45170815585936e-01, 9.44989373331317e-01,
9.44807768118372e-01, 9.44626000386548e-01, 9.44444070574127e-01, 9.44261979118237e-01,
9.44079726454850e-01, 9.43897313018794e-01, 9.43714739243752e-01, 9.43532005562268e-01,
9.43349112405755e-01, 9.43166060204493e-01, 9.42982849387641e-01, 9.42799480383237e-01,
9.42615953618203e-01, 9.42432269518352e-01, 9.42248428508389e-01, 9.42064431011918e-01,
9.41880277451445e-01, 9.41695968248383e-01, 9.41511503823058e-01, 9.41326884594710e-01,
9.41142110981499e-01, 9.40957183400510e-01, 9.40772102267757e-01, 9.40586867998187e-01,
9.40401481005683e-01, 9.40215941703071e-01, 9.40030250502120e-01, 9.39844407813550e-01,
9.39658414047037e-01, 9.39472269611212e-01, 9.39285974913668e-01, 9.39099530360966e-01,
9.38912936358635e-01, 9.38726193311179e-01, 9.38539301622081e-01, 9.38352261693803e-01,
9.38165073927797e-01, 9.37977738724502e-01, 9.37790256483351e-01, 9.37602627602776e-01,
9.37414852480209e-01, 9.37226931512088e-01, 9.37038865093859e-01, 9.36850653619983e-01,
9.36662297483937e-01, 9.36473797078216e-01, 9.36285152794341e-01, 9.36096365022861e-01,
9.35907434153356e-01, 9.35718360574442e-01, 9.35529144673771e-01, 9.35339786838040e-01,
9.35150287452990e-01, 9.34960646903414e-01, 9.34770865573156e-01, 9.34580943845116e-01,
9.34390882101256e-01, 9.34200680722601e-01, 9.34010340089242e-01, 9.33819860580341e-01,
9.33629242574135e-01, 9.33438486447937e-01, 9.33247592578141e-01, 9.33056561340226e-01,
9.32865393108756e-01, 9.32674088257389e-01, 9.32482647158875e-01, 9.32291070185061e-01,
9.32099357706898e-01, 9.31907510094437e-01, 9.31715527716838e-01, 9.31523410942371e-01,
9.31331160138421e-01, 9.31138775671488e-01, 9.30946257907193e-01, 9.30753607210281e-01,
9.30560823944620e-01, 9.30367908473211e-01, 9.30174861158187e-01, 9.29981682360816e-01,
9.29788372441503e-01, 9.29594931759798e-01, 9.29401360674395e-01, 9.29207659543133e-01,
9.29013828723006e-01, 9.28819868570159e-01, 9.28625779439896e-01, 9.28431561686678e-01,
9.28237215664132e-01, 9.28042741725048e-01, 9.27848140221386e-01, 9.27653411504277e-01,
9.27458555924027e-01, 9.27263573830120e-01, 9.27068465571217e-01, 9.26873231495166e-01,
9.26677871948997e-01, 9.26482387278932e-01, 9.26286777830382e-01, 9.26091043947953e-01,
9.25895185975449e-01, 9.25699204255872e-01, 9.25503099131427e-01, 9.25306870943525e-01,
9.25110520032784e-01, 9.24914046739034e-01, 9.24717451401316e-01, 9.24520734357888e-01,
9.24323895946228e-01, 9.24126936503033e-01, 9.23929856364226e-01, 9.23732655864954e-01,
9.23535335339596e-01, 9.23337895121761e-01, 9.23140335544292e-01, 9.22942656939269e-01,
9.22744859638014e-01, 9.22546943971087e-01, 9.22348910268294e-01, 9.22150758858690e-01,
9.21952490070576e-01, 9.21754104231508e-01, 9.21555601668294e-01, 9.21356982707002e-01,
9.21158247672955e-01, 9.20959396890742e-01, 9.20760430684214e-01, 9.20561349376489e-01,
9.20362153289955e-01, 9.20162842746271e-01, 9.19963418066368e-01, 9.19763879570456e-01,
9.19564227578022e-01, 9.19364462407834e-01, 9.19164584377944e-01, 9.18964593805690e-01,
9.18764491007695e-01, 9.18564276299875e-01, 9.18363949997439e-01, 9.18163512414888e-01,
9.17962963866022e-01, 9.17762304663940e-01, 9.17561535121041e-01, 9.17360655549031e-01,
9.17159666258919e-01, 9.16958567561024e-01, 9.16757359764974e-01, 9.16556043179710e-01,
9.16354618113490e-01, 9.16153084873885e-01, 9.15951443767789e-01, 9.15749695101414e-01,
9.15547839180298e-01, 9.15345876309304e-01, 9.15143806792621e-01, 9.14941630933769e-01,
9.14739349035602e-01, 9.14536961400303e-01, 9.14334468329396e-01, 9.14131870123741e-01,
9.13929167083538e-01, 9.13726359508330e-01, 9.13523447697004e-01, 9.13320431947793e-01,
9.13117312558278e-01, 9.12914089825393e-01, 9.12710764045421e-01, 9.12507335514002e-01,
9.12303804526130e-01, 9.12100171376160e-01, 9.11896436357805e-01, 9.11692599764142e-01,
9.11488661887612e-01, 9.11284623020021e-01, 9.11080483452544e-01, 9.10876243475726e-01,
9.10671903379485e-01, 9.10467463453110e-01, 9.10262923985270e-01, 9.10058285264007e-01,
9.09853547576747e-01, 9.09648711210294e-01, 9.09443776450838e-01, 9.09238743583951e-01,
9.09033612894596e-01, 9.08828384667121e-01, 9.08623059185267e-01, 9.08417636732168e-01,
9.08212117590350e-01, 9.08006502041737e-01, 9.07800790367650e-01, 9.07594982848811e-01,
9.07389079765341e-01, 9.07183081396768e-01, 9.06976988022023e-01, 9.06770799919442e-01,
9.06564517366773e-01, 9.06358140641172e-01, 9.06151670019209e-01, 9.05945105776866e-01,
9.05738448189541e-01, 9.05531697532050e-01, 9.05324854078628e-01, 9.05117918102929e-01,
9.04910889878031e-01, 9.04703769676436e-01, 9.04496557770071e-01, 9.04289254430290e-01,
9.04081859927877e-01, 9.03874374533047e-01, 9.03666798515446e-01, 9.03459132144156e-01,
9.03251375687693e-01, 9.03043529414010e-01, 9.02835593590501e-01, 9.02627568483997e-01,
9.02419454360776e-01, 9.02211251486555e-01, 9.02002960126500e-01, 9.01794580545221e-01,
9.01586113006778e-01, 9.01377557774682e-01, 9.01168915111893e-01, 9.00960185280827e-01,
9.00751368543352e-01, 9.00542465160795e-01, 9.00333475393939e-01, 9.00124399503028e-01,
8.99915237747765e-01, 8.99705990387317e-01, 8.99496657680313e-01, 8.99287239884851e-01,
8.99077737258492e-01, 8.98868150058268e-01, 8.98658478540680e-01, 8.98448722961702e-01,
8.98238883576777e-01, 8.98028960640828e-01, 8.97818954408249e-01, 8.97608865132913e-01,
8.97398693068174e-01, 8.97188438466862e-01, 8.96978101581293e-01, 8.96767682663263e-01,
8.96557181964053e-01, 8.96346599734432e-01, 8.96135936224654e-01, 8.95925191684464e-01,
8.95714366363095e-01, 8.95503460509274e-01, 8.95292474371218e-01, 8.95081408196641e-01,
8.94870262232752e-01, 8.94659036726257e-01, 8.94447731923361e-01, 8.94236348069768e-01,
8.94024885410685e-01, 8.93813344190820e-01, 8.93601724654385e-01, 8.93390027045099e-01,
8.93178251606186e-01, 8.92966398580380e-01, 8.92754468209921e-01, 8.92542460736563e-01,
8.92330376401570e-01, 8.92118215445721e-01, 8.91905978109309e-01, 8.91693664632142e-01,
8.91481275253545e-01, 8.91268810212365e-01, 8.91056269746965e-01, 8.90843654095229e-01,
8.90630963494568e-01, 8.90418198181911e-01, 8.90205358393716e-01, 8.89992444365964e-01,
8.89779456334167e-01, 8.89566394533364e-01, 8.89353259198122e-01, 8.89140050562543e-01,
8.88926768860259e-01, 8.88713414324436e-01, 8.88499987187775e-01, 8.88286487682515e-01,
8.88072916040429e-01, 8.87859272492832e-01, 8.87645557270576e-01, 8.87431770604056e-01,
8.87217912723208e-01, 8.87003983857513e-01, 8.86789984235994e-01, 8.86575914087222e-01,
8.86361773639315e-01, 8.86147563119938e-01, 8.85933282756306e-01, 8.85718932775184e-01,
8.85504513402890e-01, 8.85290024865294e-01, 8.85075467387819e-01, 8.84860841195444e-01,
8.84646146512706e-01, 8.84431383563698e-01, 8.84216552572070e-01, 8.84001653761034e-01,
8.83786687353363e-01, 8.83571653571390e-01, 8.83356552637013e-01, 8.83141384771694e-01,
8.82926150196459e-01, 8.82710849131902e-01, 8.82495481798185e-01, 8.82280048415036e-01,
8.82064549201755e-01, 8.81848984377213e-01, 8.81633354159853e-01, 8.81417658767688e-01,
8.81201898418310e-01, 8.80986073328883e-01, 8.80770183716148e-01, 8.80554229796424e-01,
8.80338211785607e-01, 8.80122129899175e-01, 8.79905984352184e-01, 8.79689775359272e-01,
8.79473503134662e-01, 8.79257167892157e-01, 8.79040769845149e-01, 8.78824309206612e-01,
8.78607786189110e-01, 8.78391201004792e-01, 8.78174553865398e-01, 8.77957844982256e-01,
8.77741074566288e-01, 8.77524242828005e-01, 8.77307349977512e-01, 8.77090396224509e-01,
8.76873381778289e-01, 8.76656306847743e-01, 8.76439171641358e-01, 8.76221976367219e-01,
8.76004721233010e-01, 8.75787406446016e-01, 8.75570032213121e-01, 8.75352598740812e-01,
8.75135106235180e-01, 8.74917554901918e-01, 8.74699944946326e-01, 8.74482276573308e-01,
8.74264549987375e-01, 8.74046765392646e-01, 8.73828922992851e-01, 8.73611022991326e-01,
8.73393065591019e-01, 8.73175050994492e-01, 8.72956979403915e-01, 8.72738851021076e-01,
8.72520666047374e-01, 8.72302424683826e-01, 8.72084127131063e-01, 8.71865773589334e-01,
8.71647364258508e-01, 8.71428899338069e-01, 8.71210379027126e-01, 8.70991803524405e-01,
8.70773173028255e-01, 8.70554487736648e-01, 8.70335747847180e-01, 8.70116953557071e-01,
8.69898105063165e-01, 8.69679202561936e-01, 8.69460246249481e-01, 8.69241236321528e-01,
8.69022172973433e-01, 8.68803056400183e-01, 8.68583886796393e-01, 8.68364664356312e-01,
8.68145389273822e-01, 8.67926061742436e-01, 8.67706681955303e-01, 8.67487250105206e-01,
8.67267766384566e-01, 8.67048230985439e-01, 8.66828644099520e-01, 8.66609005918140e-01,
8.66389316632273e-01, 8.66169576432530e-01, 8.65949785509166e-01, 8.65729944052076e-01,
8.65510052250799e-01, 8.65290110294516e-01, 8.65070118372054e-01, 8.64850076671886e-01,
8.64629985382128e-01, 8.64409844690545e-01, 8.64189654784551e-01, 8.63969415851207e-01,
8.63749128077224e-01, 8.63528791648962e-01, 8.63308406752433e-01, 8.63087973573302e-01,
8.62867492296885e-01, 8.62646963108153e-01, 8.62426386191728e-01, 8.62205761731892e-01,
8.61985089912579e-01, 8.61764370917381e-01, 8.61543604929548e-01, 8.61322792131987e-01,
8.61101932707265e-01, 8.60881026837609e-01, 8.60660074704905e-01, 8.60439076490704e-01,
8.60218032376214e-01, 8.59996942542310e-01, 8.59775807169530e-01, 8.59554626438074e-01,
8.59333400527811e-01, 8.59112129618273e-01, 8.58890813888660e-01, 8.58669453517840e-01,
8.58448048684348e-01, 8.58226599566389e-01, 8.58005106341838e-01, 8.57783569188239e-01,
8.57561988282809e-01, 8.57340363802437e-01, 8.57118695923683e-01, 8.56896984822782e-01,
8.56675230675644e-01, 8.56453433657851e-01, 8.56231593944665e-01, 8.56009711711020e-01,
8.55787787131530e-01, 8.55565820380486e-01, 8.55343811631858e-01, 8.55121761059296e-01,
8.54899668836127e-01, 8.54677535135363e-01, 8.54455360129695e-01, 8.54233143991497e-01,
8.54010886892824e-01, 8.53788589005418e-01, 8.53566250500703e-01, 8.53343871549788e-01,
8.53121452323469e-01, 8.52898992992228e-01, 8.52676493726234e-01, 8.52453954695342e-01,
8.52231376069099e-01, 8.52008758016739e-01, 8.51786100707187e-01, 8.51563404309056e-01,
8.51340668990654e-01, 8.51117894919978e-01, 8.50895082264720e-01, 8.50672231192263e-01,
8.50449341869685e-01, 8.50226414463759e-01, 8.50003449140953e-01, 8.49780446067432e-01,
8.49557405409054e-01, 8.49334327331380e-01, 8.49111211999663e-01, 8.48888059578860e-01,
8.48664870233624e-01, 8.48441644128308e-01, 8.48218381426968e-01, 8.47995082293358e-01,
8.47771746890937e-01, 8.47548375382865e-01, 8.47324967932005e-01, 8.47101524700924e-01,
8.46878045851894e-01, 8.46654531546892e-01, 8.46430981947600e-01, 8.46207397215409e-01,
8.45983777511413e-01, 8.45760122996416e-01, 8.45536433830931e-01, 8.45312710175179e-01,
8.45088952189090e-01, 8.44865160032305e-01, 8.44641333864176e-01, 8.44417473843766e-01,
8.44193580129849e-01, 8.43969652880914e-01, 8.43745692255161e-01, 8.43521698410506e-01,
8.43297671504579e-01, 8.43073611694723e-01, 8.42849519137998e-01, 8.42625393991183e-01,
8.42401236410770e-01, 8.42177046552970e-01, 8.41952824573714e-01, 8.41728570628648e-01,
8.41504284873141e-01, 8.41279967462279e-01, 8.41055618550871e-01, 8.40831238293445e-01,
8.40606826844253e-01, 8.40382384357267e-01, 8.40157910986184e-01, 8.39933406884423e-01,
8.39708872205127e-01, 8.39484307101164e-01, 8.39259711725128e-01, 8.39035086229339e-01,
8.38810430765841e-01, 8.38585745486407e-01, 8.38361030542538e-01, 8.38136286085460e-01,
8.37911512266132e-01, 8.37686709235240e-01, 8.37461877143198e-01, 8.37237016140154e-01,
8.37012126375985e-01, 8.36787208000299e-01, 8.36562261162437e-01, 8.36337286011473e-01,
8.36112282696213e-01, 8.35887251365197e-01, 8.35662192166700e-01, 8.35437105248732e-01,
8.35211990759036e-01, 8.34986848845095e-01, 8.34761679654124e-01, 8.34536483333079e-01,
8.34311260028651e-01, 8.34086009887271e-01, 8.33860733055106e-01, 8.33635429678064e-01,
8.33410099901794e-01, 8.33184743871682e-01, 8.32959361732858e-01, 8.32733953630192e-01,
8.32508519708294e-01, 8.32283060111520e-01, 8.32057574983967e-01, 8.31832064469476e-01,
8.31606528711630e-01, 8.31380967853759e-01, 8.31155382038937e-01, 8.30929771409985e-01,
8.30704136109467e-01, 8.30478476279696e-01, 8.30252792062732e-01, 8.30027083600382e-01,
8.29801351034200e-01, 8.29575594505492e-01, 8.29349814155309e-01, 8.29124010124455e-01,
8.28898182553483e-01, 8.28672331582697e-01, 8.28446457352150e-01, 8.28220560001650e-01,
};

static const double XK1_y2[] = {
-3.63065748466567e-07, -2.58023472807778e-07, -2.41985822720983e-07, -2.23685515081538e-07,
-2.13078660046774e-07, -2.04082461859117e-07, -1.96913586500190e-07, -1.90787664260982e-07,
-1.85491170761713e-07, -1.80812299962580e-07, -1.76626229427846e-07, -1.72838035577904e-07,
-1.69379032015306e-07, -1.66196553519764e-07, -1.63249728407422e-07, -1.60506095392892e-07,
-1.57939473581226e-07, -1.55528434603948e-07, -1.53255218653627e-07, -1.51104942866606e-07,
-1.49065012184340e-07, -1.47124672401101e-07, -1.45274669285864e-07, -1.43506981153646e-07,
-1.41814609864908e-07, -1.40191413384325e-07, -1.38631972466983e-07, -1.37131479781791e-07,
-1.35685653817474e-07, -1.34290661894268e-07, -1.32943062017306e-07, -1.31639750074595e-07,
-1.30377917552102e-07, -1.29155015237570e-07, -1.27968721754178e-07, -1.26816917872365e-07,
-1.25697663077188e-07, -1.24609176542259e-07, -1.23549819760165e-07, -1.22518081685071e-07,
-1.21512566047927e-07, -1.20531980458660e-07, -1.19575124958597e-07, -1.18640885314849e-07,
-1.17728223106678e-07, -1.16836170793326e-07, -1.15963824052853e-07, -1.15110336835804e-07,
-1.14274916948313e-07, -1.13456820910439e-07, -1.12655350073919e-07, -1.11869847645067e-07,
-1.11099695157551e-07, -1.10344308686190e-07, -1.09603138090084e-07, -1.08875662946116e-07,
-1.08161390586998e-07, -1.07459855470057e-07, -1.06770615337386e-07, -1.06093251330259e-07,
-1.05427365154067e-07, -1.04772578757844e-07, -1.04128531900915e-07, -1.03494882436800e-07,
-1.02871303614168e-07, -1.02257484264028e-07, -1.01653127419349e-07, -1.01057949432131e-07,
-1.00471679334395e-07, -9.98940578362666e-08, -9.93248371986730e-08, -9.87637797468792e-08,
-9.82106581704905e-08, -9.76652543666130e-08, -9.71273591042708e-08, -9.65967717480205e-08,
-9.60732993676077e-08, -9.55567569119901e-08, -9.50469660713215e-08, -9.45437558802337e-08,
-9.40469613317036e-08, -9.35564237663878e-08, -9.30719904793720e-08, -9.25935140164610e-08,
-9.21208526067105e-08, -9.16538690249890e-08, -9.11924313785278e-08, -9.07364118753153e-08,
-9.02856875222799e-08, -8.98401391192745e-08, -8.93996515873537e-08, -8.89641139947468e-08,
-8.85334183475336e-08, -8.81074608482538e-08, -8.76861405132845e-08, -8.72693598920063e-08,
-8.68570245719642e-08, -8.64490426626987e-08, -8.60453256899266e-08, -8.56457874223673e-08,
-8.52503446726532e-08, -8.48589159329955e-08, -8.44714231450315e-08, -8.40877897595278e-08,
-8.37079417317159e-08, -8.33318070345597e-08, -8.29593159442155e-08, -8.25904001628797e-08,
-8.22249942655823e-08, -8.18630331216327e-08, -8.15044550999050e-08, -8.11491989316793e-08,
-8.07972057265193e-08, -8.04484174876118e-08, -8.01027789251067e-08, -7.97602345739973e-08,
-7.94207319589448e-08, -7.90842188115042e-08, -7.87506450411911e-08, -7.84199609646584e-08,
-7.80921191982759e-08, -7.77670724113484e-08, -7.74447753136394e-08, -7.71251831709035e-08,
-7.68082528686547e-08, -7.64939415848495e-08, -7.61822083708525e-08, -7.58730124855587e-08,
-7.55663147031813e-08, -7.52620764125130e-08, -7.49602599136913e-08, -7.46608285759657e-08,
-7.43637463539531e-08, -7.40689781215572e-08, -7.37764895971942e-08, -7.34862471979473e-08,
-7.31982180315885e-08, -7.29123700743368e-08, -7.26286718008720e-08, -7.23470925983421e-08,
-7.20676023684971e-08, -7.17901714839035e-08, -7.15147715829949e-08, -7.12413738769465e-08,
-7.09699512413447e-08, -7.07004763165943e-08, -7.04329229067943e-08, -7.01672646152958e-08,
-6.99034765721267e-08, -6.96415334414486e-08, -6.93814108903447e-08, -6.91230853699484e-08,
-6.88665327449840e-08, -6.86117306638074e-08, -6.83586562218608e-08, -6.81072873866984e-08,
-6.78576026320328e-08, -6.76095803103873e-08, -6.73632000851525e-08, -6.71184410493531e-08,
-6.68752832666099e-08, -6.66337070412394e-08, -6.63936930756473e-08, -6.61552223486104e-08,
-6.59182760006664e-08, -6.56828361363178e-08, -6.54488843951604e-08, -6.52164034234746e-08,
-6.49853756363780e-08, -6.47557842551327e-08, -6.45276122831439e-08, -6.43008435662560e-08,
-6.40754616849932e-08, -6.38514509938322e-08, -6.36287957923184e-08, -6.34074807139477e-08,
-6.31874908877026e-08, -6.29688111250696e-08, -6.27514273450998e-08, -6.25353249067960e-08,
-6.23204897466774e-08, -6.21069081606700e-08, -6.18945664279577e-08, -6.16834512014191e-08,
-6.14735493212318e-08, -6.12648476149050e-08, -6.10573337725233e-08, -6.08509947110737e-08,
-6.06458185781568e-08, -6.04417928137082e-08, -6.02389056805539e-08, -6.00371454111362e-08,
-5.98365002026756e-08, -5.96369589787747e-08, -5.94385102352205e-08, -5.92411428975689e-08,
-5.90448463764722e-08, -5.88496095998073e-08, -5.86554221643012e-08, -5.84622736945004e-08,
-5.82701537009581e-08, -5.80790525664707e-08, -5.78889598523673e-08, -5.76998658682685e-08,
-5.75117613056100e-08, -5.73246361345866e-08, -5.71384813852523e-08, -5.69532875670680e-08,
-5.67690456568953e-08, -5.65857467258764e-08, -5.64033818888085e-08, -5.62219422136337e-08,
-5.60414195781924e-08, -5.58618049990554e-08, -5.56830903516174e-08, -5.55052674907592e-08,
-5.53283279386830e-08, -5.51522641247302e-08, -5.49770677358768e-08, -5.48027311891534e-08,
-5.46292467221387e-08, -5.44566067822102e-08, -5.42848039341570e-08, -5.41138305074131e-08,
-5.39436795443983e-08, -5.37743436913907e-08, -5.36058160221603e-08, -5.34380890738069e-08,
-5.32711565475082e-08, -5.31050111334246e-08, -5.29396464033064e-08, -5.27750555229858e-08,
-5.26112319562875e-08, -5.24481693801853e-08, -5.22858612092429e-08, -5.21243012504259e-08,
-5.19634831137252e-08, -5.18034010266733e-08, -5.16440482758789e-08, -5.14854195177471e-08,
-5.13275084231352e-08, -5.11703092368937e-08, -5.10138162257157e-08, -5.08580236610647e-08,
-5.07029258845016e-08, -5.05485171744730e-08, -5.03947924358735e-08, -5.02417457962552e-08,
-5.00893722007575e-08, -4.99376659888923e-08, -4.97866223279376e-08, -4.96362357891589e-08,
-4.94865012788599e-08, -4.93374137363603e-08, -4.91889683000115e-08, -4.90411598341331e-08,
-4.88939834340070e-08, -4.87474346553201e-08, -4.86015080914007e-08, -4.84561997262047e-08,
-4.83115042742054e-08, -4.81674175836655e-08, -4.80239347906864e-08, -4.78810516360015e-08,
-4.77387634862456e-08, -4.75970659336822e-08, -4.74559548193144e-08, -4.73154256517366e-08,
-4.71754741322604e-08, -4.70360963008928e-08, -4.68972877603658e-08, -4.67590444135921e-08,
-4.66213623992381e-08, -4.64842373899302e-08, -4.63476655764785e-08, -4.62116430973102e-08,
-4.60761656711783e-08, -4.59412300817817e-08, -4.58068318262234e-08, -4.56729675964628e-08,
-4.55396334782107e-08, -4.54068257881144e-08, -4.52745409694141e-08, -4.51427751721303e-08,
-4.50115250374574e-08, -4.48807870894272e-08, -4.47505573854585e-08, -4.46208330784055e-08,
-4.44916101815524e-08, -4.43628856175148e-08, -4.42346560315983e-08, -4.41069177139054e-08,
-4.39796679865285e-08, -4.38529030633376e-08, -4.37266200055894e-08, -4.36008153695739e-08,
-4.34754863289486e-08, -4.33506294251363e-08, -4.32262418898850e-08, -4.31023201581452e-08,
-4.29788618294636e-08, -4.28558634173573e-08, -4.27333219503311e-08, -4.26112349262574e-08,
-4.24895987828191e-08, -4.23684112865987e-08, -4.22476689463712e-08, -4.21273694197299e-08,
-4.20075096913374e-08, -4.18880868454710e-08, -4.17690984629236e-08, -4.16505414821021e-08,
-4.15324134711516e-08, -4.14147114539179e-08, -4.12974331135269e-08, -4.11805755945964e-08,
-4.10641363152506e-08, -4.09481128042302e-08, -4.08325024294154e-08, -4.07173026474223e-08,
-4.06025110538505e-08, -4.04881249326974e-08, -4.03741422312957e-08, -4.02605599985298e-08,
-4.01473763263620e-08, -4.00345883643605e-08, -3.99221941012121e-08, -3.98101909989030e-08,
-3.96985767879023e-08, -3.95873490955372e-08, -3.94765058042424e-08, -3.93660443232527e-08,
-3.92559628113172e-08, -3.91462587897071e-08, -3.90369300257788e-08, -3.89279744951362e-08,
-3.88193899824871e-08, -3.87111741617429e-08, -3.86033252298735e-08, -3.84958407346796e-08,
-3.83887188542899e-08, -3.82819573379796e-08, -3.81755542429552e-08, -3.80695074896843e-08,
-3.79638150156140e-08, -3.78584748270132e-08, -3.77534850819726e-08, -3.76488435955410e-08,
-3.75445485149349e-08, -3.74405980009423e-08, -3.73369899389198e-08, -3.72337225252217e-08,
-3.71307939868444e-08, -3.70282022282401e-08, -3.69259455252168e-08, -3.68240221009273e-08,
-3.67224299067666e-08, -3.66211673676823e-08, -3.65202326184376e-08, -3.64196238148461e-08,
-3.63193392076823e-08, -3.62193772019386e-08, -3.61197357128183e-08, -3.60204134612639e-08,
-3.59214083224286e-08, -3.58227190835487e-08, -3.57243433946528e-08, -3.56262803220709e-08,
-3.55285276237813e-08, -3.54310840993108e-08, -3.53339476887450e-08, -3.52371171740734e-08,
-3.51405908275133e-08, -3.50443668972209e-08, -3.49484440153246e-08, -3.48528205233706e-08,
-3.47574948751272e-08, -3.46624654770793e-08, -3.45677310346683e-08, -3.44732897709262e-08,
-3.43791402072991e-08, -3.42852811531858e-08, -3.41917105228722e-08, -3.40984276357646e-08,
-3.40054303055469e-08, -3.39127176330026e-08, -3.38202878517976e-08, -3.37281396006114e-08,
-3.36362715423425e-08, -3.35446823931118e-08, -3.34533702988642e-08, -3.33623345228042e-08,
-3.32715730938080e-08, -3.31810850852483e-08, -3.30908689583085e-08, -3.30009232461647e-08,
-3.29112470282567e-08, -3.28218384592443e-08, -3.27326967372197e-08, -3.26438201427935e-08,
-3.25552075846695e-08, -3.24668579309723e-08, -3.23787694730275e-08, -3.22909414066463e-08,
-3.22033722179646e-08, -3.21160607730220e-08, -3.20290056830299e-08, -3.19422059765641e-08,
-3.18556602667720e-08, -3.17693671899046e-08, -3.16833260382943e-08, -3.15975350111557e-08,
-3.15119934705811e-08, -3.14266997737822e-08, -3.13416532472364e-08, -3.12568521215956e-08,
-3.11722959321246e-08, -3.10879829780417e-08, -3.10039124225812e-08, -3.09200830963380e-08,
-3.08364937413385e-08, -3.07531434534543e-08, -3.06700311119681e-08, -3.05871552204955e-08,
-3.05045154467965e-08, -3.04221099532790e-08, -3.03399382069009e-08, -3.02579987373301e-08,
-3.01762909645320e-08, -3.00948132388839e-08, -3.00135651893950e-08, -2.99325450646701e-08,
-2.98517524697193e-08, -2.97711860729606e-08, -2.96908448233517e-08, -2.96107279283725e-08,
-2.95308340580304e-08, -2.94511626634781e-08, -2.93717123851159e-08, -2.92924823268070e-08,
-2.92134716595390e-08, -2.91346792664272e-08, -2.90561042267742e-08, -2.89777456781167e-08,
-2.88996024398905e-08, -2.88216738795665e-08, -2.87439588228441e-08, -2.86664564932283e-08,
-2.85891657309064e-08, -2.85120860674424e-08, -2.84352159844789e-08, -2.83585551404987e-08,
-2.82821023121024e-08, -2.82058567392006e-08, -2.81298173564797e-08, -2.80539836341688e-08,
-2.79783543157730e-08, -2.79029286287709e-08, -2.78277060347623e-08, -2.77526851299993e-08,
-2.76778655175580e-08, -2.76032460810566e-08, -2.75288261318313e-08, -2.74546047669599e-08,
-2.73805810687470e-08, -2.73067543928477e-08, -2.72331239044677e-08, -2.71596884801029e-08,
-2.70864476754045e-08, -2.70134006165134e-08, -2.69405462472113e-08, -2.68678841151150e-08,
-2.67954132001952e-08, -2.67231327058821e-08, -2.66510421755470e-08, -2.65791402354720e-08,
-2.65074268419530e-08, -2.64359005459222e-08, -2.63645609701057e-08, -2.62934075199532e-08,
-2.62224387320924e-08, -2.61516548373141e-08, -2.60810541553810e-08, -2.60106366261358e-08,
-2.59404011728429e-08, -2.58703471665983e-08, -2.58004738698841e-08, -2.57307805318058e-08,
-2.56612665635896e-08, -2.55919309633998e-08, -2.55227734423716e-08, -2.54537928271313e-08,
-2.53849888819901e-08, -2.53163605034301e-08, -2.52479073452081e-08, -2.51796283431012e-08,
-2.51115232152627e-08, -2.50435910446777e-08, -2.49758311183161e-08, -2.49082429864659e-08,
-2.48408257193135e-08, -2.47735788228886e-08, -2.47065016501724e-08, -2.46395933974296e-08,
-2.45728535967508e-08, -2.45062813707948e-08, -2.44398763669664e-08, -2.43736376533404e-08,
-2.43075648693209e-08, -2.42416570585479e-08, -2.41759139661651e-08, -2.41103345703552e-08,
-2.40449186613297e-08, -2.39796652134795e-08, -2.39145739871155e-08, -2.38496439690012e-08,
-2.37848750108794e-08, -2.37202660544800e-08, -2.36558169292263e-08, -2.35915266001375e-08,
-2.35273948257996e-08, -2.34634208312912e-08, -2.33996040719317e-08, -2.33359440596736e-08,
-2.32724399607180e-08, -2.32090914904829e-08, -2.31458978455381e-08, -2.30828586384055e-08,
-2.30199731138030e-08, -2.29572409055795e-08, -2.28946612360187e-08, -2.28322338073786e-08,
-2.27699577017640e-08, -2.27078327806725e-08, -2.26458581845402e-08, -2.25840334933223e-08,
-2.25223581381377e-08, -2.24608315949086e-08, -2.23994533091809e-08, -2.23382226921793e-08,
-2.22771394338121e-08, -2.22162025876645e-08, -2.21554120306399e-08, -2.20947672031375e-08,
-2.20342671359882e-08, -2.19739119355993e-08, -2.19137007022213e-08, -2.18536329316414e-08,
-2.17937083208139e-08, -2.17339261436439e-08, -2.16742860548425e-08, -2.16147873861029e-08,
-2.15554299362946e-08, -2.14962127357554e-08, -2.14371357564395e-08, -2.13781983038359e-08,
-2.13193998533648e-08, -2.12607399782097e-08, -2.12022181346587e-08, -2.11438340377965e-08,
-2.10855868174831e-08, -2.10274765754577e-08, -2.09695021095691e-08, -2.09116636857909e-08,
-2.08539603321564e-08, -2.07963916737562e-08, -2.07389575176592e-08, -2.06816570120982e-08,
-2.06244899823141e-08, -2.05674558696875e-08, -2.05105541968748e-08, -2.04537845452900e-08,
-2.03971464020853e-08, -2.03406395727029e-08, -2.02842631277760e-08, -2.02280172045707e-08,
-2.01719008511220e-08, -2.01159139632656e-08, -2.00600559112220e-08, -2.00043264316940e-08,
-1.99487249872039e-08, -1.98932509933574e-08, -1.98379044386293e-08, -1.97826845102248e-08,
-1.97275909181348e-08, -1.96726233037223e-08, -1.96177811710982e-08, -1.95630640868981e-08,
-1.95084717269561e-08, -1.94540036008539e-08, -1.93996592188731e-08, -1.93454385878149e-08,
-1.92913405048586e-08, -1.92373655556383e-08, -1.91835123783933e-08, -1.91297813936406e-08,
-1.90761716149389e-08, -1.90226829038002e-08, -1.89693148022168e-08, -1.89160670602612e-08,
-1.88629390262275e-08, -1.88099304482423e-08, -1.87570410981260e-08, -1.87042702530910e-08,
-1.86516178128206e-08, -1.85990832360347e-08, -1.85466662346573e-08, -1.84943663928494e-08,
-1.84421833305738e-08, -1.83901166523506e-08, -1.83381659886680e-08, -1.82863311036295e-08,
-1.82346114229532e-08, -1.81830067041062e-08, -1.81315164931006e-08, -1.80801405169519e-08,
-1.80288785452298e-08, -1.79777296632162e-08, -1.79266943185222e-08, -1.78757714133769e-08,
-1.78249611164947e-08, -1.77742628515882e-08, -1.77236760905572e-08, -1.76732009685766e-08,
-1.76228365848692e-08, -1.75725830766997e-08, -1.75224396855630e-08, -1.74724064216354e-08,
-1.74224825594267e-08, -1.73726683261863e-08, -1.73229626502281e-08, -1.72733658162892e-08,
-1.72238772019952e-08, -1.71744964585943e-08, -1.71252233830216e-08, -1.70760575819765e-08,
-1.70269986112802e-08, -1.69780464205024e-08, -1.69292003232756e-08, -1.68804603399423e-08,
-1.68318258542549e-08, -1.67832968683706e-08, -1.67348726576404e-08, -1.66865532319234e-08,
-1.66383381662091e-08, -1.65902270412567e-08, -1.65422197385941e-08, -1.64943158190823e-08,
-1.64465149373038e-08, -1.63988169156659e-08, -1.63512212556448e-08, -1.63037279084825e-08,
-1.62563362354666e-08, -1.62090462866924e-08, -1.61618575012904e-08, -1.61147696301520e-08,
-1.60677824542247e-08, -1.60208956555373e-08, -1.59741087266252e-08, -1.59274217948723e-08,
-1.58808340810514e-08, -1.58343456881073e-08, -1.57879559842879e-08, -1.57416650621879e-08,
-1.56954722950023e-08, -1.56493774328212e-08, -1.56033804367545e-08, -1.55574807130719e-08,
-1.55116782330940e-08, -1.54659724840237e-08, -1.54203634363049e-08, -1.53748503886912e-08,
-1.53294337332337e-08, -1.52841123809299e-08, -1.52388867430250e-08, -1.51937561525185e-08,
-1.51487204236761e-08, -1.51037794121240e-08, -1.50589325488236e-08, -1.50141799228349e-08,
-1.49695209698005e-08, -1.49249556376436e-08, -1.48804833667613e-08, -1.48361043382182e-08,
-1.47918177212252e-08, -1.47476237712943e-08, -1.47035219640995e-08, -1.46595120320087e-08,
-1.46155936824978e-08, -1.45717669100050e-08, -1.45280311411234e-08, -1.44843862325513e-08,
-1.44408319986353e-08, -1.43973681040453e-08, -1.43539942993983e-08, -1.43107103632436e-08,
-1.42675159874776e-08, -1.42244109606306e-08, -1.41813951044175e-08, -1.41384679001587e-08,
-1.40956294914336e-08, -1.40528792674928e-08, -1.40102171962860e-08, -1.39676430175632e-08,
-1.39251562500628e-08, -1.38827571917015e-08, -1.38404447990076e-08, -1.37982196172820e-08,
-1.37560809528817e-08, -1.37140285925877e-08, -1.36720625286061e-08, -1.36301822281761e-08,
-1.35883877207107e-08, -1.35466785331403e-08, -1.35050546409511e-08, -1.34635156160673e-08,
-1.34220614189489e-08, -1.33806916366313e-08, -1.33394061841558e-08, -1.32982047040989e-08,
-1.32570870457785e-08, -1.32160529481013e-08, -1.31751022738550e-08, -1.31342346117369e-08,
-1.30934498567909e-08, -1.30527478409433e-08, -1.30121282312217e-08, -1.29715907512331e-08,
-1.29311353962318e-08, -1.28907617954598e-08, -1.28504695493155e-08, -1.28102589616287e-08,
-1.27701292166821e-08, -1.27300804979573e-08, -1.26901123321339e-08, -1.26502248746995e-08,
-1.26104173108902e-08, -1.25706900797391e-08, -1.25310424619219e-08, -1.24914745642347e-08,
-1.24519860126832e-08, -1.24125765311142e-08, -1.23732462658671e-08, -1.23339944636482e-08,
-1.22948214377801e-08, -1.22557265772439e-08, -1.22167100143910e-08, -1.21777711647008e-08,
-1.21389102355031e-08, -1.21001266489320e-08, -1.20614205107202e-08, -1.20227914206913e-08,
-1.19842390974615e-08, -1.19457637344744e-08, -1.19073646172946e-08, -1.18690419677300e-08,
-1.18307952799173e-08, -1.17926245791447e-08, -1.17545296039893e-08, -1.17165100425866e-08,
-1.16785657384829e-08, -1.16406967411795e-08, -1.16029024540133e-08, -1.15651829936889e-08,
-1.15275380459620e-08, -1.14899673078152e-08, -1.14524709732949e-08, -1.14150482361662e-08,
-1.13776995738090e-08, -1.13404243270280e-08, -1.13032224347781e-08, -1.12660936902124e-08,
-1.12290382046076e-08, -1.11920551845920e-08, -1.11551450278402e-08, -1.11183071590704e-08,
-1.10815417053784e-08, -1.10448481785513e-08, -1.10082265169659e-08, -1.09716767891936e-08,
-1.09351982274605e-08, -1.08987913918006e-08, -1.08624553649634e-08, -1.08261904803587e-08,
-1.07899964326205e-08, -1.07538728885578e-08, -1.07178198209657e-08, -1.06818371167438e-08,
-1.06459242562972e-08, -1.06100815437271e-08, -1.05743085042683e-08, -1.05386048455013e-08,
-1.05029707685792e-08, -1.04674058723317e-08, -1.04319098949517e-08, -1.03964828415484e-08,
-1.03611245094031e-08, -1.03258347050802e-08, -1.02906130727736e-08, -1.02554598968754e-08,
-1.02203743956236e-08, -1.01853570802053e-08, -1.01504071317237e-08, -1.01155248720879e-08,
-1.00807098325584e-08, -1.00459620118721e-08, -1.00112812176871e-08, -9.97666722143331e-09,
-9.94211979746517e-09, -9.90763907773430e-09, -9.87322453803522e-09, -9.83887625585913e-09,
-9.80459389033523e-09, -9.77037761723247e-09, -9.73622663025663e-09, -9.70214164734727e-09,
-9.66812160224110e-09, -9.63416704444958e-09, -9.60027750832398e-09, -9.56645264161322e-09,
-9.53269287568038e-09, -9.49899739243575e-09, -9.46536636833986e-09, -9.43179980461793e-09,
-9.39829707581940e-09, -9.36485846207525e-09, -9.33148369035670e-09, -9.29817235140254e-09,
-9.26492480097421e-09, -9.23174024733171e-09, -9.19861917020527e-09, -9.16556099752548e-09,
-9.13256565046064e-09, -9.09963312822848e-09, -9.06676317972291e-09, -9.03395558890524e-09,
-9.00121036081331e-09, -8.96852713622287e-09, -8.93590612574782e-09, -8.90334662411218e-09,
-8.87084913238221e-09, -8.83841290668038e-09, -8.80603831202679e-09, -8.77372474324086e-09,
-8.74147247966801e-09, -8.70928100910715e-09, -8.67715043568261e-09, -8.64508052203135e-09,
-8.61307111428039e-09, -8.58112206608399e-09, -8.54923333954197e-09, -8.51740456646703e-09,
-8.48563592524090e-09, -8.45392695950160e-09, -8.42227776200311e-09, -8.39068797400232e-09,
-8.35915771647235e-09, -8.32768664221920e-09, -8.29627468677811e-09, -8.26492167804604e-09,
-8.23362770276610e-09, -8.20239203095735e-09, -8.17121538637670e-09, -8.14009682522276e-09,
-8.10903673440896e-09, -8.07803473212752e-09, -8.04709073745087e-09, -8.01620478976320e-09,
-7.98537625734386e-09, -7.95460574031208e-09, -7.92389246911232e-09, -7.89323659037915e-09,
-7.86263784304062e-09, -7.83209656963846e-09, -7.80161166107770e-09, -7.77118410257204e-09,
-7.74081294974078e-09, -7.71049844138002e-09, -7.68024034464149e-09, -7.65003868598836e-09,
-7.61989292628238e-09, -7.58980353027888e-09, -7.55976984422856e-09, -7.52979201997189e-09,
-7.49986988185170e-09, -7.47000320350003e-09, -7.44019206684516e-09, -7.41043603747509e-09,
-7.38073532781955e-09, -7.35108963359393e-09, -7.32149873826160e-09, -7.29196270203072e-09,
-7.26248138958297e-09, -7.23305450482730e-09, -7.20368203517864e-09, -7.17436399400140e-09,
-7.14510000735608e-09, -7.11589000332410e-09, -7.08673408840770e-09, -7.05763190851653e-09,
-7.02858333021984e-09, -6.99958846417480e-09, -6.97064689016123e-09, -6.94175873511274e-09,
-6.91292380049279e-09, -6.88414186533548e-09, -6.85541290181790e-09, -6.82673690913070e-09,
-6.79811347424499e-09, -6.76954280679576e-09, -6.74102448127194e-09, -6.71255865781519e-09,
-6.68414501034761e-09, -6.65578357281614e-09, -6.62747420244398e-09, -6.59921654821302e-09,
-6.57101093572712e-09, -6.54285685767821e-09, -6.51475435236015e-09, -6.48670344083864e-09,
-6.45870366749016e-09, -6.43075527943082e-09, -6.40285796586432e-09, -6.37501161263674e-09,
-6.34721621000389e-09, -6.31947157802960e-09, -6.29177755802428e-09, -6.26413418752636e-09,
-6.23654114200484e-09, -6.20899857182221e-09, -6.18150620005951e-09, -6.15406376278479e-09,
-6.12667159344407e-09, -6.09932917729676e-09, -6.07203657452462e-09, -6.04479361505200e-09,
-6.01760036388829e-09, -5.99045639800461e-09, -5.96336190121717e-09, -5.93631667231231e-09,
-5.90932044415004e-09, -5.88237348730324e-09, -5.85547520866505e-09, -5.82862593373314e-09,
-5.80182528669059e-09, -5.77507333508441e-09, -5.74836985147656e-09, -5.72171467887148e-09,
-5.69510800655561e-09, -5.66854934540110e-09, -5.64203890832064e-09, -5.61557633279132e-09,
-5.58916185679135e-09, -5.56279489093085e-09, -5.53647577843426e-09, -5.51020429090522e-09,
-5.48398011052630e-09, -5.45780351571823e-09, -5.43167393266016e-09, -5.40559182390256e-09,
-5.37955657919815e-09, -5.35356840062874e-09, -5.32762697909212e-09, -5.30173257175920e-09,
-5.27588457007081e-09, -5.25008337473586e-09, -5.22432843556715e-09, -5.19862010931463e-09,
-5.17295785223261e-09, -5.14734192824161e-09, -5.12177204744989e-09, -5.09624810630317e-09,
-5.07077014277652e-09, -5.04533788647928e-09, -5.01995138179828e-09, -4.99461049953233e-09,
-4.96931504596549e-09, -4.94406503698433e-09, -4.91886049173622e-09, -4.89370087365583e-09,
-4.86858664452259e-09, -4.84351727094026e-09, -4.81849298142444e-09, -4.79351339530895e-09,
-4.76857869651990e-09, -4.74368853001902e-09, -4.71884302181028e-09, -4.69404191189372e-09,
-4.66928522608681e-09, -4.64457278805272e-09, -4.61990461118752e-09, -4.59528048517681e-09,
-4.57070034970371e-09, -4.54616421226094e-09, -4.52167177012758e-09, -4.49722322749388e-09,
-4.47281818134205e-09, -4.44845681830770e-09, -4.42413890588847e-09, -4.39986418825746e-09,
-4.37563303304619e-09, -4.35144489168934e-09, -4.32729992548209e-09, -4.30319792678678e-09,
-4.27913900974731e-09, -4.25512270338119e-09, -4.23114933418452e-09, -4.20721862226689e-09,
-4.18333036149311e-09, -4.15948476811595e-09, -4.13568140530414e-09, -4.11192058288465e-09,
-4.08820172042547e-09, -4.06452527551542e-09, -4.04089066436509e-09, -4.01729821023103e-09,
-3.99374753694335e-09, -3.97023871570203e-09, -3.94677161583248e-09, -3.92334613372157e-09,
-3.89996214836252e-09, -3.87661980330643e-09, -3.85331864535568e-09, -3.83005890045970e-09,
};

/*
 * Lookup tables for 0 < u <= 1/q.  u values are scaled so that the table
 * abscissas are integers from 0 to 511.
 */

static const double XK1_v[] = {
0.00000000000000e+00, 2.04935502333971e-221, 1.70612668724056e-110, 1.47167880061809e-73,
4.14405177065441e-55, 4.74618820274473e-44, 1.10096994065064e-36, 1.98468814733909e-31,
1.72114303273418e-27, 1.97627844006864e-24, 5.51464272428044e-22, 5.50298555841575e-20,
2.54040692336905e-18, 6.48358240903852e-17, 1.03893629597892e-15, 1.14744574102514e-14,
9.36731608290833e-14, 5.96286218574994e-13, 3.08533642749686e-12, 1.34092658171943e-11,
5.02522711600971e-11, 1.65872691036812e-10, 4.90686346773335e-10, 1.31968639068115e-09,
3.26560238045128e-09, 7.50997101588147e-09, 1.61875357795678e-08, 3.29404023788093e-08,
6.36754024620018e-08, 1.17551031802688e-07, 2.08209630480894e-07, 3.55257164477340e-07,
5.85978355448963e-07, 9.37260373593791e-07, 1.45768512799353e-06, 2.20973937467797e-06,
3.27208409753221e-06, 4.74182023362280e-06, 6.73668682338950e-06, 9.39712981478352e-06,
1.28881845952992e-05, 1.74011223069538e-05, 2.31548185076231e-05, 3.03968121750774e-05,
3.94040328524350e-05, 5.04831834250534e-05, 6.39707752079715e-05, 8.02328204126344e-05,
9.96641944453434e-05, 1.22687686743799e-04, 1.49752763929507e-04, 1.81334072948352e-04,
2.17929714640371e-04, 2.60059319906889e-04, 3.08261961435276e-04, 3.63093933918017e-04,
4.25126434988311e-04, 4.94943177812908e-04, 5.73137964552970e-04, 6.60312247835664e-04,
7.57072705072528e-04, 8.64028848003363e-04, 9.81790687312565e-04, 1.11096646962211e-03,
1.25216052423894e-03, 1.40597110859103e-03, 1.57298854668913e-03, 1.75379331873879e-03,
1.94895434596694e-03, 2.15902739870117e-03, 2.38455362488540e-03, 2.62605821654492e-03,
2.88404920210303e-03, 3.15901637251568e-03, 3.45143033235054e-03, 3.76174167191660e-03,
4.09038026412359e-03, 4.43775467153449e-03, 4.80425166695299e-03, 5.19023585595981e-03,
5.59604940018728e-03, 6.02201183281193e-03, 6.46841996229512e-03, 6.93554785660153e-03,
7.42364690183055e-03, 7.93294593394192e-03, 8.46365143050278e-03, 9.01594776278675e-03,
9.58999750060299e-03, 1.01859417646288e-02, 1.08039006220827e-02, 1.14439735188789e-02,
1.21062397471748e-02, 1.27907589411685e-02, 1.34975715978621e-02, 1.42266996199523e-02,
1.49781468759214e-02, 1.57518997751780e-02, 1.65479278542486e-02, 1.73661843720828e-02,
1.82066069108709e-02, 1.90691179805013e-02, 1.99536256249902e-02, 2.08600240273753e-02,
2.17881941127510e-02, 2.27380041468754e-02, 2.37093103292157e-02, 2.47019573789562e-02,
2.57157791127509e-02, 2.67505990134023e-02, 2.78062307882235e-02, 2.88824789163042e-02,
2.99791391842959e-02, 3.10959992098406e-02, 3.22328389519983e-02, 3.33894312087182e-02,
3.45655421006086e-02, 3.57609315409620e-02, 3.69753536916908e-02, 3.82085574051506e-02,
3.94602866518928e-02, 4.07302809339296e-02, 4.20182756839751e-02, 4.33240026504690e-02,
4.46471902685641e-02, 4.59875640171658e-02, 4.73448467622868e-02, 4.87187590867836e-02,
5.01090196067783e-02, 5.15153452749480e-02, 5.29374516709686e-02, 5.43750532793405e-02,
5.58278637549326e-02, 5.72955961764455e-02, 5.87779632881417e-02, 6.02746777302188e-02,
6.17854522579609e-02, 6.33099999501078e-02, 6.48480344067403e-02, 6.63992699369734e-02,
6.79634217368077e-02, 6.95402060573093e-02, 7.11293403637131e-02, 7.27305434854514e-02,
7.43435357576368e-02, 7.59680391541340e-02, 7.76037774127332e-02, 7.92504761524429e-02,
8.09078629834161e-02, 8.25756676097004e-02, 8.42536219250847e-02, 8.59414601023311e-02,
8.76389186760241e-02, 8.93457366193872e-02, 9.10616554151750e-02, 9.27864191210195e-02,
9.45197744293551e-02, 9.62614707222685e-02, 9.80112601213932e-02, 9.97688975331265e-02,
1.01534140689342e-01, 1.03306750183876e-01, 1.05086489504866e-01, 1.06873125063236e-01,
1.08666426217462e-01, 1.10466165294829e-01, 1.12272117609294e-01, 1.14084061476189e-01,
1.15901778223894e-01, 1.17725052202601e-01, 1.19553670790401e-01, 1.21387424396733e-01,
1.23226106463416e-01, 1.25069513463368e-01, 1.26917444897118e-01, 1.28769703287262e-01,
1.30626094170970e-01, 1.32486426090654e-01, 1.34350510582904e-01, 1.36218162165811e-01,
1.38089198324740e-01, 1.39963439496695e-01, 1.41840709053330e-01, 1.43720833282714e-01,
1.45603641369905e-01, 1.47488965376474e-01, 1.49376640218967e-01, 1.51266503646461e-01,
1.53158396217223e-01, 1.55052161274580e-01, 1.56947644922035e-01, 1.58844695997704e-01,
1.60743166048124e-01, 1.62642909301502e-01, 1.64543782640421e-01, 1.66445645574109e-01,
1.68348360210257e-01, 1.70251791226480e-01, 1.72155805841432e-01, 1.74060273785639e-01,
1.75965067272060e-01, 1.77870060966446e-01, 1.79775131957511e-01, 1.81680159726941e-01,
1.83585026119295e-01, 1.85489615311817e-01, 1.87393813784168e-01, 1.89297510288144e-01,
1.91200595817365e-01, 1.93102963576985e-01, 1.95004508953431e-01, 1.96905129484200e-01,
1.98804724827728e-01, 2.00703196733351e-01, 2.02600449011376e-01, 2.04496387503285e-01,
2.06390920052067e-01, 2.08283956472715e-01, 2.10175408522892e-01, 2.12065189873774e-01,
2.13953216081082e-01, 2.15839404556334e-01, 2.17723674538284e-01, 2.19605947064615e-01,
2.21486144943832e-01, 2.23364192727417e-01, 2.25240016682220e-01, 2.27113544763106e-01,
2.28984706585856e-01, 2.30853433400336e-01, 2.32719658063943e-01, 2.34583315015310e-01,
2.36444340248297e-01, 2.38302671286265e-01, 2.40158247156634e-01, 2.42011008365719e-01,
2.43860896873878e-01, 2.45707856070923e-01, 2.47551830751848e-01, 2.49392767092842e-01,
2.51230612627599e-01, 2.53065316223923e-01, 2.54896828060634e-01, 2.56725099604773e-01,
2.58550083589098e-01, 2.60371733989879e-01, 2.62190006005001e-01, 2.64004856032345e-01,
2.65816241648477e-01, 2.67624121587631e-01, 2.69428455720981e-01, 2.71229205036205e-01,
2.73026331617348e-01, 2.74819798624960e-01, 2.76609570276534e-01, 2.78395611827221e-01,
2.80177889550839e-01, 2.81956370721148e-01, 2.83731023593418e-01, 2.85501817386270e-01,
2.87268722263787e-01, 2.89031709317906e-01, 2.90790750551072e-01, 2.92545818859166e-01,
2.94296888014694e-01, 2.96043932650236e-01, 2.97786928242163e-01, 2.99525851094606e-01,
3.01260678323674e-01, 3.02991387841936e-01, 3.04717958343136e-01, 3.06440369287170e-01,
3.08158600885294e-01, 3.09872634085577e-01, 3.11582450558590e-01, 3.13288032683331e-01,
3.14989363533382e-01, 3.16686426863288e-01, 3.18379207095170e-01, 3.20067689305556e-01,
3.21751859212436e-01, 3.23431703162525e-01, 3.25107208118752e-01, 3.26778361647949e-01,
3.28445151908759e-01, 3.30107567639738e-01, 3.31765598147667e-01, 3.33419233296063e-01,
3.35068463493886e-01, 3.36713279684437e-01, 3.38353673334452e-01, 3.39989636423380e-01,
3.41621161432854e-01, 3.43248241336334e-01, 3.44870869588937e-01, 3.46489040117449e-01,
3.48102747310500e-01, 3.49711986008921e-01, 3.51316751496266e-01, 3.52917039489504e-01,
3.54512846129873e-01, 3.56104167973894e-01, 3.57691001984552e-01, 3.59273345522626e-01,
3.60851196338172e-01, 3.62424552562172e-01, 3.63993412698315e-01, 3.65557775614933e-01,
3.67117640537087e-01, 3.68673007038787e-01, 3.70223875035354e-01, 3.71770244775922e-01,
3.73312116836079e-01, 3.74849492110633e-01, 3.76382371806514e-01, 3.77910757435808e-01,
3.79434650808912e-01, 3.80954054027818e-01, 3.82468969479520e-01, 3.83979399829537e-01,
3.85485348015562e-01, 3.86986817241220e-01, 3.88483810969950e-01, 3.89976332918991e-01,
3.91464387053483e-01, 3.92947977580678e-01, 3.94427108944258e-01, 3.95901785818755e-01,
3.97372013104078e-01, 3.98837795920146e-01, 4.00299139601607e-01, 4.01756049692673e-01,
4.03208531942041e-01, 4.04656592297910e-01, 4.06100236903095e-01, 4.07539472090228e-01,
4.08974304377058e-01, 4.10404740461826e-01, 4.11830787218742e-01, 4.13252451693536e-01,
4.14669741099100e-01, 4.16082662811208e-01, 4.17491224364322e-01, 4.18895433447475e-01,
4.20295297900231e-01, 4.21690825708727e-01, 4.23082025001784e-01, 4.24468904047097e-01,
4.25851471247498e-01, 4.27229735137287e-01, 4.28603704378640e-01, 4.29973387758079e-01,
4.31338794183014e-01, 4.32699932678351e-01, 4.34056812383165e-01, 4.35409442547442e-01,
4.36757832528873e-01, 4.38101991789726e-01, 4.39441929893764e-01, 4.40777656503232e-01,
4.42109181375901e-01, 4.43436514362169e-01, 4.44759665402217e-01, 4.46078644523226e-01,
4.47393461836646e-01, 4.48704127535512e-01, 4.50010651891828e-01, 4.51313045253987e-01,
4.52611318044255e-01, 4.53905480756294e-01, 4.55195543952742e-01, 4.56481518262838e-01,
4.57763414380093e-01, 4.59041243060014e-01, 4.60315015117864e-01, 4.61584741426472e-01,
4.62850432914093e-01, 4.64112100562295e-01, 4.65369755403908e-01, 4.66623408521000e-01,
4.67873071042900e-01, 4.69118754144260e-01, 4.70360469043157e-01, 4.71598226999234e-01,
4.72832039311877e-01, 4.74061917318432e-01, 4.75287872392455e-01, 4.76509915942003e-01,
4.77728059407957e-01, 4.78942314262377e-01, 4.80152692006898e-01, 4.81359204171155e-01,
4.82561862311239e-01, 4.83760678008190e-01, 4.84955662866517e-01, 4.86146828512755e-01,
4.87334186594042e-01, 4.88517748776739e-01, 4.89697526745069e-01, 4.90873532199790e-01,
4.92045776856892e-01, 4.93214272446330e-01, 4.94379030710772e-01, 4.95540063404388e-01,
4.96697382291649e-01, 4.97850999146167e-01, 4.99000925749552e-01, 5.00147173890293e-01,
5.01289755362669e-01, 5.02428681965678e-01, 5.03563965501994e-01, 5.04695617776942e-01,
5.05823650597504e-01, 5.06948075771336e-01, 5.08068905105816e-01, 5.09186150407106e-01,
5.10299823479244e-01, 5.11409936123249e-01, 5.12516500136244e-01, 5.13619527310612e-01,
5.14719029433153e-01, 5.15815018284278e-01, 5.16907505637207e-01, 5.17996503257194e-01,
5.19082022900770e-01, 5.20164076314996e-01, 5.21242675236743e-01, 5.22317831391984e-01,
5.23389556495100e-01, 5.24457862248209e-01, 5.25522760340508e-01, 5.26584262447626e-01,
5.27642380231001e-01, 5.28697125337269e-01, 5.29748509397659e-01, 5.30796544027421e-01,
5.31841240825252e-01, 5.32882611372739e-01, 5.33920667233826e-01, 5.34955419954281e-01,
5.35986881061184e-01, 5.37015062062428e-01, 5.38039974446229e-01, 5.39061629680651e-01,
5.40080039213143e-01, 5.41095214470088e-01, 5.42107166856364e-01, 5.43115907754914e-01,
5.44121448526333e-01, 5.45123800508462e-01, 5.46122975015988e-01, 5.47118983340070e-01,
5.48111836747957e-01, 5.49101546482632e-01, 5.50088123762452e-01, 5.51071579780813e-01,
5.52051925705811e-01, 5.53029172679921e-01, 5.54003331819680e-01, 5.54974414215388e-01,
5.55942430930803e-01, 5.56907393002861e-01, 5.57869311441394e-01, 5.58828197228860e-01,
5.59784061320081e-01, 5.60736914641989e-01, 5.61686768093382e-01, 5.62633632544683e-01,
5.63577518837710e-01, 5.64518437785456e-01, 5.65456400171871e-01, 5.66391416751653e-01,
5.67323498250049e-01, 5.68252655362658e-01, 5.69178898755246e-01, 5.70102239063564e-01,
5.71022686893173e-01, 5.71940252819277e-01, 5.72854947386562e-01, 5.73766781109036e-01,
5.74675764469886e-01, 5.75581907921332e-01, 5.76485221884483e-01, 5.77385716749216e-01,
5.78283402874040e-01, 5.79178290585978e-01, 5.80070390180452e-01, 5.80959711921170e-01,
5.81846266040025e-01, 5.82730062736986e-01, 5.83611112180012e-01, 5.84489424504954e-01,
5.85365009815472e-01, 5.86237878182951e-01, 5.87108039646427e-01, 5.87975504212513e-01,
5.88840281855328e-01, 5.89702382516437e-01, 5.90561816104788e-01, 5.91418592496659e-01,
5.92272721535600e-01, 5.93124213032392e-01, 5.93973076764999e-01, 5.94819322478527e-01,
5.95662959885189e-01, 5.96503998664269e-01, 5.97342448462096e-01, 5.98178318892012e-01,
5.99011619534353e-01, 5.99842359936430e-01, 6.00670549612506e-01, 6.01496198043791e-01,
6.02319314678424e-01, 6.03139908931471e-01, 6.03957990184914e-01, 6.04773567787658e-01,
6.05586651055523e-01, 6.06397249271256e-01, 6.07205371684529e-01, 6.08011027511955e-01,
6.08814225937097e-01, 6.09614976110481e-01, 6.10413287149616e-01, 6.11209168139007e-01,
6.12002628130183e-01, 6.12793676141716e-01, 6.13582321159248e-01, 6.14368572135520e-01,
6.15152437990400e-01, 6.15933927610917e-01, 6.16713049851294e-01, 6.17489813532986e-01,
6.18264227444714e-01, 6.19036300342509e-01, 6.19806040949753e-01, 6.20573457957219e-01,
6.21338560023122e-01, 6.22101355773163e-01, 6.22861853800576e-01, 6.23620062666181e-01,
6.24375990898436e-01, 6.25129646993488e-01, 6.25881039415230e-01, 6.26630176595356e-01,
6.27377066933423e-01, 6.28121718796901e-01, 6.28864140521246e-01, 6.29604340409950e-01,
6.30342326734612e-01, 6.31078107735000e-01, 6.31811691619116e-01, 6.32543086563265e-01,
6.33272300712119e-01, 6.33999342178790e-01, 6.34724219044901e-01, 6.35446939360651e-01,
6.36167511144894e-01, 6.36885942385210e-01, 6.37602241037979e-01, 6.38316415028455e-01,
6.39028472250845e-01, 6.39738420568384e-01, 6.40446267813415e-01, 6.41152021787463e-01,
6.41855690261322e-01, 6.42557280975128e-01, 6.43256801638445e-01, 6.43954259930345e-01,
6.44649663499491e-01, 6.45343019964221e-01, 6.46034336912630e-01, 6.46723621902656e-01,
6.47410882462165e-01, 6.48096126089038e-01, 6.48779360251256e-01, 6.49460592386987e-01,
6.50139829904674e-01, 6.50817080183123e-01, 6.51492350571593e-01, 6.52165648389883e-01,
6.52836980928422e-01, 6.53506355448359e-01, 6.54173779181655e-01, 6.54839259331172e-01,
6.55502803070766e-01, 6.56164417545376e-01, 6.56824109871119e-01, 6.57481887135380e-01,
6.58137756396907e-01, 6.58791724685902e-01, 6.59443799004116e-01, 6.60093986324940e-01,
6.60742293593502e-01, 6.61388727726760e-01, 6.62033295613595e-01, 6.62676004114909e-01,
6.63316860063716e-01, 6.63955870265239e-01, 6.64593041497006e-01, 6.65228380508944e-01,
6.65861894023475e-01, 6.66493588735613e-01, 6.67123471313059e-01, 6.67751548396295e-01,
6.68377826598684e-01, 6.69002312506564e-01, 6.69625012679346e-01, 6.70245933649608e-01,
6.70865081923194e-01, 6.71482463979309e-01, 6.72098086270616e-01, 6.72711955223336e-01,
6.73324077237338e-01, 6.73934458686242e-01, 6.74543105917515e-01, 6.75150025252564e-01,
6.75755222986837e-01, 6.76358705389919e-01, 6.76960478705626e-01, 6.77560549152106e-01,
6.78158922921934e-01, 6.78755606182208e-01, 6.79350605074647e-01, 6.79943925715687e-01,
6.80535574196580e-01, 6.81125556583484e-01, 6.81713878917569e-01, 6.82300547215105e-01,
6.82885567467564e-01, 6.83468945641714e-01, 6.84050687679713e-01, 6.84630799499211e-01,
6.85209286993439e-01, 6.85786156031311e-01, 6.86361412457515e-01, 6.86935062092613e-01,
6.87507110733131e-01, 6.88077564151660e-01, 6.88646428096947e-01, 6.89213708293993e-01,
6.89779410444145e-01, 6.90343540225194e-01, 6.90906103291467e-01, 6.91467105273922e-01,
6.92026551780245e-01, 6.92584448394939e-01, 6.93140800679422e-01, 6.93695614172117e-01,
6.94248894388553e-01, 6.94800646821447e-01, 6.95350876940808e-01, 6.95899590194023e-01,
6.96446792005954e-01, 6.96992487779026e-01, 6.97536682893323e-01, 6.98079382706680e-01,
6.98620592554773e-01, 6.99160317751212e-01, 6.99698563587632e-01, 7.00235335333785e-01,
7.00770638237629e-01, 7.01304477525421e-01, 7.01836858401808e-01, 7.02367786049913e-01,
7.02897265631430e-01, 7.03425302286714e-01, 7.03951901134864e-01, 7.04477067273820e-01,
7.05000805780449e-01, 7.05523121710633e-01, 7.06044020099359e-01, 7.06563505960806e-01,
7.07081584288434e-01, 7.07598260055073e-01, 7.08113538213009e-01, 7.08627423694070e-01,
7.09139921409718e-01, 7.09651036251128e-01, 7.10160773089283e-01, 7.10669136775055e-01,
7.11176132139291e-01, 7.11681763992902e-01, 7.12186037126944e-01, 7.12688956312708e-01,
7.13190526301801e-01, 7.13690751826234e-01, 7.14189637598501e-01, 7.14687188311669e-01,
7.15183408639459e-01, 7.15678303236329e-01, 7.16171876737559e-01, 7.16664133759333e-01,
7.17155078898819e-01, 7.17644716734258e-01, 7.18133051825039e-01, 7.18620088711785e-01,
7.19105831916433e-01, 7.19590285942316e-01, 7.20073455274242e-01, 7.20555344378580e-01,
7.21035957703331e-01, 7.21515299678219e-01, 7.21993374714761e-01, 7.22470187206354e-01,
7.22945741528349e-01, 7.23420042038134e-01, 7.23893093075208e-01, 7.24364898961264e-01,
7.24835464000264e-01, 7.25304792478519e-01, 7.25772888664764e-01, 7.26239756810235e-01,
7.26705401148750e-01, 7.27169825896781e-01, 7.27633035253533e-01, 7.28095033401018e-01,
7.28555824504133e-01, 7.29015412710732e-01, 7.29473802151705e-01, 7.29930996941051e-01,
7.30387001175952e-01, 7.30841818936847e-01, 7.31295454287509e-01, 7.31747911275115e-01,
7.32199193930319e-01, 7.32649306267330e-01, 7.33098252283979e-01, 7.33546035961796e-01,
7.33992661266079e-01, 7.34438132145967e-01, 7.34882452534511e-01, 7.35325626348749e-01,
7.35767657489771e-01, 7.36208549842793e-01, 7.36648307277229e-01, 7.37086933646757e-01,
7.37524432789394e-01, 7.37960808527560e-01, 7.38396064668151e-01, 7.38830205002608e-01,
7.39263233306984e-01, 7.39695153342013e-01, 7.40125968853177e-01, 7.40555683570779e-01,
7.40984301210002e-01, 7.41411825470985e-01, 7.41838260038884e-01, 7.42263608583940e-01,
7.42687874761547e-01, 7.43111062212319e-01, 7.43533174562152e-01, 7.43954215422290e-01,
7.44374188389398e-01, 7.44793097045614e-01, 7.45210944958625e-01, 7.45627735681727e-01,
7.46043472753888e-01, 7.46458159699815e-01, 7.46871800030014e-01, 7.47284397240857e-01,
7.47695954814642e-01, 7.48106476219658e-01, 7.48515964910248e-01, 7.48924424326867e-01,
7.49331857896149e-01, 7.49738269030967e-01, 7.50143661130494e-01, 7.50548037580262e-01,
7.50951401752228e-01, 7.51353757004830e-01, 7.51755106683052e-01, 7.52155454118477e-01,
7.52554802629354e-01, 7.52953155520655e-01, 7.53350516084133e-01, 7.53746887598381e-01,
7.54142273328894e-01, 7.54536676528124e-01, 7.54930100435539e-01, 7.55322548277684e-01,
7.55714023268233e-01, 7.56104528608053e-01, 7.56494067485256e-01, 7.56882643075257e-01,
7.57270258540834e-01, 7.57656917032181e-01, 7.58042621686966e-01, 7.58427375630383e-01,
7.58811181975216e-01, 7.59194043821885e-01, 7.59575964258507e-01, 7.59956946360950e-01,
7.60336993192886e-01, 7.60716107805848e-01, 7.61094293239281e-01, 7.61471552520597e-01,
7.61847888665232e-01, 7.62223304676696e-01, 7.62597803546624e-01, 7.62971388254836e-01,
7.63344061769383e-01, 7.63715827046602e-01, 7.64086687031170e-01, 7.64456644656154e-01,
7.64825702843060e-01, 7.65193864501892e-01, 7.65561132531196e-01, 7.65927509818115e-01,
7.66292999238438e-01, 7.66657603656651e-01, 7.67021325925988e-01, 7.67384168888482e-01,
7.67746135375011e-01, 7.68107228205352e-01, 7.68467450188227e-01, 7.68826804121356e-01,
7.69185292791502e-01, 7.69542918974522e-01, 7.69899685435415e-01, 7.70255594928370e-01,
7.70610650196815e-01, 7.70964853973462e-01, 7.71318208980359e-01, 7.71670717928935e-01,
7.72022383520046e-01, 7.72373208444024e-01, 7.72723195380721e-01, 7.73072346999562e-01,
7.73420665959581e-01, 7.73768154909477e-01, 7.74114816487653e-01, 7.74460653322268e-01,
7.74805668031273e-01, 7.75149863222467e-01, 7.75493241493534e-01, 7.75835805432092e-01,
7.76177557615736e-01, 7.76518500612083e-01, 7.76858636978815e-01, 7.77197969263724e-01,
7.77536500004756e-01, 7.77874231730054e-01, 7.78211166958002e-01, 7.78547308197265e-01,
7.78882657946838e-01, 7.79217218696083e-01, 7.79550992924775e-01, 7.79883983103141e-01,
7.80216191691906e-01, 7.80547621142334e-01, 7.80878273896267e-01, 7.81208152386168e-01,
7.81537259035166e-01, 7.81865596257091e-01, 7.82193166456517e-01, 7.82519972028808e-01,
7.82846015360150e-01, 7.83171298827598e-01, 7.83495824799112e-01, 7.83819595633600e-01,
7.84142613680957e-01, 7.84464881282103e-01, 7.84786400769023e-01, 7.85107174464809e-01,
7.85427204683696e-01, 7.85746493731101e-01, 7.86065043903664e-01, 7.86382857489283e-01,
7.86699936767157e-01, 7.87016284007819e-01, 7.87331901473178e-01, 7.87646791416554e-01,
7.87960956082719e-01, 7.88274397707928e-01, 7.88587118519966e-01, 7.88899120738176e-01,
7.89210406573500e-01, 7.89520978228516e-01, 7.89830837897473e-01, 7.90139987766329e-01,
7.90448430012785e-01, 7.90756166806323e-01, 7.91063200308243e-01, 7.91369532671694e-01,
7.91675166041715e-01, 7.91980102555265e-01, 7.92284344341263e-01, 7.92587893520622e-01,
7.92890752206280e-01, 7.93192922503240e-01, 7.93494406508600e-01, 7.93795206311591e-01,
7.94095323993610e-01, 7.94394761628252e-01, 7.94693521281346e-01, 7.94991605010990e-01,
7.95289014867580e-01, 7.95585752893849e-01, 7.95881821124895e-01, 7.96177221588218e-01,
7.96471956303751e-01, 7.96766027283894e-01, 7.97059436533544e-01, 7.97352186050132e-01,
7.97644277823649e-01, 7.97935713836685e-01, 7.98226496064455e-01, 7.98516626474837e-01,
7.98806107028397e-01, 7.99094939678425e-01, 7.99383126370965e-01, 7.99670669044847e-01,
7.99957569631718e-01, 8.00243830056071e-01, 8.00529452235277e-01, 8.00814438079618e-01,
8.01098789492315e-01, 8.01382508369557e-01, 8.01665596600534e-01, 8.01948056067468e-01,
8.02229888645638e-01, 8.02511096203415e-01, 8.02791680602289e-01, 8.03071643696898e-01,
8.03350987335060e-01, 8.03629713357800e-01, 8.03907823599380e-01, 8.04185319887326e-01,
8.04462204042461e-01, 8.04738477878930e-01, 8.05014143204230e-01, 8.05289201819237e-01,
8.05563655518238e-01, 8.05837506088955e-01, 8.06110755312573e-01, 8.06383404963774e-01,
8.06655456810755e-01, 8.06926912615265e-01, 8.07197774132626e-01, 8.07468043111764e-01,
8.07737721295234e-01, 8.08006810419249e-01, 8.08275312213705e-01, 8.08543228402210e-01,
8.08810560702108e-01, 8.09077310824510e-01, 8.09343480474314e-01, 8.09609071350238e-01,
8.09874085144842e-01, 8.10138523544556e-01, 8.10402388229703e-01, 8.10665680874530e-01,
8.10928403147230e-01, 8.11190556709967e-01, 8.11452143218906e-01, 8.11713164324233e-01,
8.11973621670181e-01, 8.12233516895062e-01, 8.12492851631281e-01, 8.12751627505371e-01,
8.13009846138011e-01, 8.13267509144053e-01, 8.13524618132547e-01, 8.13781174706766e-01,
8.14037180464229e-01, 8.14292636996724e-01, 8.14547545890335e-01, 8.14801908725464e-01,
8.15055727076857e-01, 8.15309002513623e-01, 8.15561736599265e-01, 8.15813930891696e-01,
8.16065586943266e-01, 8.16316706300788e-01, 8.16567290505555e-01, 8.16817341093369e-01,
8.17066859594558e-01, 8.17315847534006e-01, 8.17564306431169e-01, 8.17812237800103e-01,
8.18059643149483e-01, 8.18306523982626e-01, 8.18552881797516e-01, 8.18798718086821e-01,
8.19044034337923e-01, 8.19288832032931e-01, 8.19533112648709e-01, 8.19776877656897e-01,
8.20020128523930e-01, 8.20262866711065e-01, 8.20505093674394e-01, 8.20746810864874e-01,
8.20988019728345e-01, 8.21228721705548e-01, 8.21468918232152e-01, 8.21708610738771e-01,
8.21947800650986e-01, 8.22186489389367e-01, 8.22424678369490e-01, 8.22662369001962e-01,
8.22899562692442e-01, 8.23136260841654e-01, 8.23372464845417e-01, 8.23608176094660e-01,
8.23843395975442e-01, 8.24078125868973e-01, 8.24312367151636e-01, 8.24546121195001e-01,
8.24779389365854e-01, 8.25012173026207e-01, 8.25244473533325e-01, 8.25476292239740e-01,
8.25707630493275e-01, 8.25938489637060e-01, 8.26168871009554e-01, 8.26398775944562e-01,
8.26628205771254e-01, 8.26857161814185e-01, 8.27085645393315e-01, 8.27313657824026e-01,
8.27541200417140e-01, 8.27768274478940e-01, 8.27994881311186e-01, 8.28221022211137e-01,
};

static const double XK1_v2[] = {
0.00000000000000e+00, -2.35022087391863e-28, 8.22577305871522e-28, -3.05528713609422e-27,
1.13985712385053e-26, -4.25389978179273e-26, 1.58757420034304e-25, -5.92490483852679e-25,
2.21292526147261e-24, -6.28637420956580e-24, 5.70446008267730e-22, 5.16534056588802e-20,
2.22371460782937e-18, 5.08635282622549e-17, 7.06127227064670e-16, 6.58604820586301e-15,
4.47128622540427e-14, 2.34976857105044e-13, 1.00181686050174e-12, 3.59263488166359e-12,
1.11467195660492e-11, 3.05979013879520e-11, 7.56549107419503e-11, 1.70968843815539e-10,
3.57385659858204e-10, 6.97941162411711e-10, 1.28404581875112e-09, 2.24117739813893e-09,
3.73337807264412e-09, 5.96593956877832e-09, 9.18583298976284e-09, 1.36796637904094e-08,
1.97691688237763e-08, 2.78044880876914e-08, 3.81556150803717e-08, 5.12025438755205e-08,
6.73246855873457e-08, 8.68901270114457e-08, 1.10245260042976e-07, 1.37705234443973e-07,
1.69545591302824e-07, 2.05995331483663e-07, 2.47231571777129e-07, 2.93375848192902e-07,
3.44492045354528e-07, 4.00585865649781e-07, 4.61605702346066e-07, 5.27444746710706e-07,
5.97944138857317e-07, 6.72896963607157e-07, 7.52052893965896e-07, 8.35123293665775e-07,
9.21786604545128e-07, 1.01169386265319e-06, 1.10447420671133e-06, 1.19974026485476e-06,
1.29709332142297e-06, 1.39612820375654e-06, 1.49643777901508e-06, 1.59761722281618e-06,
1.69926728388929e-06, 1.80099933559771e-06, 1.90243175208749e-06, 2.00321665639685e-06,
2.10297392961329e-06, 2.20141736040021e-06, 2.29821037479914e-06, 2.39307509196829e-06,
2.48574443581634e-06, 2.57597267083987e-06, 2.66353833083145e-06, 2.74823948111786e-06,
2.82989764329098e-06, 2.90835480025451e-06, 2.98347257790945e-06, 3.05513461929926e-06,
3.12324158582365e-06, 3.18771424132326e-06, 3.24848945647111e-06, 3.30552152111678e-06,
3.35877967971916e-06, 3.40824815717771e-06, 3.45392455011741e-06, 3.49581846556759e-06,
3.53395251021980e-06, 3.56835837591153e-06, 3.59907843561627e-06, 3.62616360474098e-06,
3.64967267767797e-06, 3.66967189417307e-06, 3.68623317362647e-06, 3.69943475370125e-06,
3.70935931119510e-06, 3.71609369944139e-06, 3.71972859078205e-06, 3.72035733412437e-06,
3.71807595164515e-06, 3.71298214667693e-06, 3.70517527578854e-06, 3.69475551360681e-06,
3.68182362386001e-06, 3.66648083316703e-06, 3.64882790189643e-06, 3.62896545556250e-06,
3.60699326642766e-06, 3.58301022736591e-06, 3.55711404014120e-06, 3.52940101211852e-06,
3.49996596563424e-06, 3.46890198208248e-06, 3.43630027581656e-06, 3.40225017412260e-06,
3.36683893875928e-06, 3.33015162376196e-06, 3.29227117924978e-06, 3.25327822144212e-06,
3.21325110551209e-06, 3.17226581942799e-06, 3.13039599216161e-06, 3.08771294297029e-06,
3.04428551841548e-06, 3.00018027786769e-06, 2.95546137883297e-06, 2.91019065527014e-06,
2.86442760126609e-06, 2.81822944623173e-06, 2.77165113309371e-06, 2.72474539720179e-06,
2.67756277604962e-06, 2.63015167347050e-06, 2.58255838107000e-06, 2.53482715359163e-06,
2.48700022465354e-06, 2.43911786871324e-06, 2.39121848371603e-06, 2.34333857737226e-06,
2.29551287173857e-06, 2.24777434047734e-06, 2.20015425201437e-06, 2.15268225201182e-06,
2.10538634114251e-06, 2.05829305073147e-06, 2.01142735811962e-06, 1.96481285138549e-06,
1.91847168326926e-06, 1.87242472749278e-06, 1.82669150868997e-06, 1.78129034822251e-06,
1.73623836192541e-06, 1.69155151528028e-06, 1.64724467680102e-06, 1.60333163975215e-06,
1.55982521072058e-06, 1.51673718746604e-06, 1.47407846412737e-06, 1.43185901267344e-06,
1.39008797637690e-06, 1.34877365953943e-06, 1.30792359681133e-06, 1.26754456174531e-06,
1.22764263855204e-06, 1.18822320313624e-06, 1.14929100406578e-06, 1.11085016019505e-06,
1.07290421232606e-06, 1.03545613082676e-06, 9.98508362296410e-07, 9.62062850335917e-07,
9.26121046050104e-07, 8.90683967267938e-07, 8.55752178255447e-07, 8.21325851153873e-07,
7.87404768609482e-07, 7.53988344131204e-07, 7.21075652119568e-07, 6.88665440659599e-07,
6.56756150198740e-07, 6.25345934302894e-07, 5.94432678885366e-07, 5.64014007064161e-07,
5.34087314139380e-07, 5.04649762908740e-07, 4.75698314834611e-07, 4.47229726272952e-07,
4.19240587180029e-07, 3.91727302145395e-07, 3.64686129579412e-07, 3.38113178877780e-07,
3.12004424348059e-07, 2.86355718369548e-07, 2.61162799656287e-07, 2.36421297921145e-07,
2.12126758665094e-07, 1.88274625703623e-07, 1.64860280193341e-07, 1.41879021847729e-07,
1.19326093057108e-07, 9.71966798523281e-08, 7.54859179028627e-08, 5.41889019776578e-08,
3.33006890383208e-08, 1.28163075750263e-08, -7.26924147449000e-09, -2.69609763650173e-08,
-4.62639282961138e-08, -6.51831434547544e-08, -8.37236685747308e-08, -1.01890557279235e-07,
-1.19688857402524e-07, -1.37123613866091e-07, -1.54199860859513e-07, -1.70922620153840e-07,
-1.87296899596714e-07, -2.03327686940717e-07, -2.19019949472777e-07, -2.34378631703939e-07,
-2.49408651158595e-07, -2.64114897238482e-07, -2.78502230235238e-07, -2.92575477811960e-07,
-3.06339431634708e-07, -3.19798852735355e-07, -3.32958458424669e-07, -3.45822933555728e-07,
-3.58396920262027e-07, -3.70685018181948e-07, -3.82691788521461e-07, -3.94421745683479e-07,
-4.05879364039183e-07, -4.17069067484531e-07, -4.27995239435125e-07, -4.38662214995089e-07,
-4.49074281109191e-07, -4.59235679011513e-07, -4.69150602438799e-07, -4.78823193751903e-07,
-4.88257550300971e-07, -4.97457718386371e-07, -5.06427695562186e-07, -5.15171430375650e-07,
-5.23692820994895e-07, -5.31995718182951e-07, -5.40083919103877e-07, -5.47961176773021e-07,
-5.55631189294261e-07, -5.63097608480782e-07, -5.70364036396290e-07, -5.77434024629681e-07,
-5.84311076658356e-07, -5.90998646669807e-07, -5.97500140746227e-07, -6.03818915413893e-07,
-6.09958279763045e-07, -6.15921495857458e-07, -6.21711775753450e-07, -6.27332286685993e-07,
-6.32786147738170e-07, -6.38076431315889e-07, -6.43206164964964e-07, -6.48178328012645e-07,
-6.52995857189219e-07, -6.57661641655423e-07, -6.62178528389393e-07, -6.66549317435349e-07,
-6.70776768360955e-07, -6.74863594611301e-07, -6.78812467867237e-07, -6.82626018526040e-07,
-6.86306832418002e-07, -6.89857458019319e-07, -6.93280397537288e-07, -6.96578117704101e-07,
-6.99753041939758e-07, -7.02807555752092e-07, -7.05744004853138e-07, -7.08564696238918e-07,
-7.11271900527891e-07, -7.13867847467065e-07, -7.16354733186912e-07, -7.18734714882458e-07,
-7.21009914397901e-07, -7.23182417922316e-07, -7.25254276342250e-07, -7.27227505689964e-07,
-7.29104088495043e-07, -7.30885972093090e-07, -7.32575072485000e-07, -7.34173270694203e-07,
-7.35682417871800e-07, -7.37104330342650e-07, -7.38440796488810e-07, -7.39693570045872e-07,
-7.40864377710712e-07, -7.41954913732832e-07, -7.42966843449630e-07, -7.43901803935365e-07,
-7.44761402144389e-07, -7.45547217692455e-07, -7.46260802303486e-07, -7.46903679962862e-07,
-7.47477347634632e-07, -7.47983276458248e-07, -7.48422909963656e-07, -7.48797668459881e-07,
-7.49108943313120e-07, -7.49358104621108e-07, -7.49546495721982e-07, -7.49675436437735e-07,
-7.49746222641439e-07, -7.49760127575994e-07, -7.49718400453583e-07, -7.49622268518655e-07,
-7.49472936746868e-07, -7.49271588096541e-07, -7.49019383581072e-07, -7.48717464336831e-07,
-7.48366949107838e-07, -7.47968936965612e-07, -7.47524507382779e-07, -7.47034718606570e-07,
-7.46500610760562e-07, -7.45923204279055e-07, -7.45303500403303e-07, -7.44642483093663e-07,
-7.43941116435900e-07, -7.43200347941262e-07, -7.42421107154751e-07, -7.41604306478647e-07,
-7.40750840269365e-07, -7.39861588514672e-07, -7.38937412076273e-07, -7.37979157717181e-07,
-7.36987655350688e-07, -7.35963719909281e-07, -7.34908149895166e-07, -7.33821730865159e-07,
-7.32705230989729e-07, -7.31559406172588e-07, -7.30384996725337e-07, -7.29182729165517e-07,
-7.27953316957178e-07, -7.26697458859187e-07, -7.25415841238697e-07, -7.24109137185830e-07,
-7.22778006464707e-07, -7.21423097316295e-07, -7.20045043958929e-07, -7.18644470397985e-07,
-7.17221986846019e-07, -7.15778193182610e-07, -7.14313676743975e-07, -7.12829014151949e-07,
-7.11324770815879e-07, -7.09801500818498e-07, -7.08259747981579e-07, -7.06700045325656e-07,
-7.05122915554865e-07, -7.03528871212169e-07, -7.01918414794871e-07, -7.00292039247551e-07,
-6.98650227262597e-07, -6.96993453030009e-07, -6.95322180156522e-07, -6.93636864575562e-07,
-6.91937952038228e-07, -6.90225880298895e-07, -6.88501077600283e-07, -6.86763965048773e-07,
-6.85014953957143e-07, -6.83254448269648e-07, -6.81482843902725e-07, -6.79700528457513e-07,
-6.77907882196385e-07, -6.76105277477428e-07, -6.74293079429357e-07, -6.72471645593740e-07,
-6.70641326625680e-07, -6.68802465736223e-07, -6.66955399500419e-07, -6.65100457514123e-07,
-6.63237962736698e-07, -6.61368231462588e-07, -6.59491573925008e-07, -6.57608293130840e-07,
-6.55718687252037e-07, -6.53823046665194e-07, -6.51921657406662e-07, -6.50014798528170e-07,
-6.48102743557085e-07, -6.46185760685931e-07, -6.44264112219382e-07, -6.42338054931444e-07,
-6.40407840688537e-07, -6.38473715542861e-07, -6.36535920515427e-07, -6.34594692257119e-07,
-6.32650261009215e-07, -6.30702853714858e-07, -6.28752691328685e-07, -6.26799990693703e-07,
-6.24844963887476e-07, -6.22887818405388e-07, -6.20928757358978e-07, -6.18967979498518e-07,
-6.17005679090909e-07, -6.15042046663072e-07, -6.13077267871342e-07, -6.11111525337593e-07,
-6.09144996376651e-07, -6.07177855865135e-07, -6.05210273588986e-07, -6.03242416599935e-07,
-6.01274446994017e-07, -5.99306525110381e-07, -5.97338805618866e-07, -5.95371441311148e-07,
-5.93404580841393e-07, -5.91438369531592e-07, -5.89472949630825e-07, -5.87508460027177e-07,
-5.85545036363653e-07, -5.83582811306685e-07, -5.81621914466433e-07, -5.79662472225009e-07,
-5.77704608392262e-07, -5.75748443641797e-07, -5.73794095778851e-07, -5.71841680009911e-07,
-5.69891308706603e-07, -5.67943091636428e-07, -5.65997135720007e-07, -5.64053545882396e-07,
-5.62112423444891e-07, -5.60173868708895e-07, -5.58237978223848e-07, -5.56304846692333e-07,
-5.54374566966730e-07, -5.52447228490531e-07, -5.50522919539647e-07, -5.48601725477990e-07,
-5.46683729941126e-07, -5.44769014066532e-07, -5.42857657056641e-07, -5.40949736472766e-07,
-5.39045327051469e-07, -5.37144502258582e-07, -5.35247333364572e-07, -5.33353889590677e-07,
-5.31464238893064e-07, -5.29578446456431e-07, -5.27696576715790e-07, -5.25818691549703e-07,
-5.23944851488730e-07, -5.22075115463977e-07, -5.20209540493424e-07, -5.18348182077849e-07,
-5.16491094263069e-07, -5.14638329328112e-07, -5.12789938193150e-07, -5.10945970209795e-07,
-5.09106473258931e-07, -5.07271493791124e-07, -5.05441076789210e-07, -5.03615266099563e-07,
-5.01794103810575e-07, -4.99977631075195e-07, -4.98165887440702e-07, -4.96358911374807e-07,
-4.94556740163728e-07, -4.92759409238686e-07, -4.90966954083672e-07, -4.89179407496717e-07,
-4.87396802308781e-07, -4.85619169797251e-07, -4.83846539649307e-07, -4.82078941583948e-07,
-4.80316403008349e-07, -4.78558951219288e-07, -4.76806612048106e-07, -4.75059410414908e-07,
-4.73317370132931e-07, -4.71580514469930e-07, -4.69848865208509e-07, -4.68122443622947e-07,
-4.66401269732014e-07, -4.64685363089637e-07, -4.62974742034762e-07, -4.61269424013845e-07,
-4.59569426151254e-07, -4.57874764088473e-07, -4.56185453059260e-07, -4.54501507636416e-07,
-4.52822941003393e-07, -4.51149766566801e-07, -4.49481995787463e-07, -4.47819640802825e-07,
-4.46162711546328e-07, -4.44511218874363e-07, -4.42865171045300e-07, -4.41224577904068e-07,
-4.39589446546574e-07, -4.37959784818511e-07, -4.36335599316260e-07, -4.34716896442769e-07,
-4.33103681404377e-07, -4.31495959391294e-07, -4.29893734967473e-07, -4.28297011554290e-07,
-4.26705792995725e-07, -4.25120081699743e-07, -4.23539879955671e-07, -4.21965189964998e-07,
-4.20396012178766e-07, -4.18832348142432e-07, -4.17274197773439e-07, -4.15721560855763e-07,
-4.14174436892760e-07, -4.12632824867390e-07, -4.11096723016183e-07, -4.09566129751119e-07,
-4.08041042307565e-07, -4.06521458344057e-07, -4.05007374447962e-07, -4.03498787071357e-07,
-4.01995692502278e-07, -4.00498086154892e-07, -3.99005963550160e-07, -3.97519319767568e-07,
-3.96038149214232e-07, -3.94562446319597e-07, -3.93092205096971e-07, -3.91627419203467e-07,
-3.90168081805655e-07, -3.88714186279050e-07, -3.87265724987786e-07, -3.85822690690896e-07,
-3.84385075246126e-07, -3.82952870945911e-07, -3.81526068912152e-07, -3.80104660961486e-07,
-3.78688637857249e-07, -3.77277990550576e-07, -3.75872709739596e-07, -3.74472785614396e-07,
-3.73078208429791e-07, -3.71688968023590e-07, -3.70305054060542e-07, -3.68926456093399e-07,
-3.67553163296756e-07, -3.66185164804504e-07, -3.64822449292300e-07, -3.63465005755136e-07,
-3.62112822257868e-07, -3.60765887491010e-07, -3.59424189238707e-07, -3.58087715731415e-07,
-3.56756454542760e-07, -3.55430393317949e-07, -3.54109519628607e-07, -3.52793820713996e-07,
-3.51483283551078e-07, -3.50177895610194e-07, -3.48877643205588e-07, -3.47582513451838e-07,
-3.46292492861579e-07, -3.45007567778525e-07, -3.43727724824808e-07, -3.42452949899868e-07,
-3.41183229406059e-07, -3.39918549122909e-07, -3.38658895153006e-07, -3.37404253151565e-07,
-3.36154608796941e-07, -3.34909947678211e-07, -3.33670255607412e-07, -3.32435517260942e-07,
-3.31205718859240e-07, -3.29980844912891e-07, -3.28760880897981e-07, -3.27545811914812e-07,
-3.26335622713135e-07, -3.25130298599441e-07, -3.23929824003021e-07, -3.22734184084774e-07,
-3.21543363288635e-07, -3.20357346418437e-07, -3.19176118110483e-07, -3.17999662756202e-07,
-3.16827965005862e-07, -3.15661009163337e-07, -3.14498779882087e-07, -3.13341261096683e-07,
-3.12188437491311e-07, -3.11040293135930e-07, -3.09896812364489e-07, -3.08757979180228e-07,
-3.07623777979105e-07, -3.06494192583048e-07, -3.05369207607164e-07, -3.04248806289111e-07,
-3.03132973585573e-07, -3.02021692729335e-07, -3.00914948243966e-07, -2.99812723767313e-07,
-2.98715003412972e-07, -2.97621771165443e-07, -2.96533010605772e-07, -2.95448706169737e-07,
-2.94368841165023e-07, -2.93293400003443e-07, -2.92222366139857e-07, -2.91155723643383e-07,
-2.90093456415328e-07, -2.89035548191949e-07, -2.87981982760351e-07, -2.86932744313387e-07,
-2.85887816147224e-07, -2.84847182740623e-07, -2.83810827403198e-07, -2.82778734385038e-07,
-2.81750887341882e-07, -2.80727270145145e-07, -2.79707866841981e-07, -2.78692661116022e-07,
-2.77681637041074e-07, -2.76674778381946e-07, -2.75672069194143e-07, -2.74673493345523e-07,
-2.73679034719751e-07, -2.72688677435926e-07, -2.71702405432759e-07, -2.70720202690997e-07,
-2.69742053092601e-07, -2.68767941094691e-07, -2.67797850173781e-07, -2.66831765044220e-07,
-2.65869669225192e-07, -2.64911547336202e-07, -2.63957383233139e-07, -2.63007161171715e-07,
-2.62060865460147e-07, -2.61118480240896e-07, -2.60179989600815e-07, -2.59245378348000e-07,
-2.58314630126531e-07, -2.57387729961787e-07, -2.56464661626595e-07, -2.55545409969174e-07,
-2.54629959231224e-07, -2.53718293894900e-07, -2.52810398531152e-07, -2.51906257670401e-07,
-2.51005855805363e-07, -2.50109177731139e-07, -2.49216207848136e-07, -2.48326931056004e-07,
-2.47441331873359e-07, -2.46559395288599e-07, -2.45681105902250e-07, -2.44806448619390e-07,
-2.43935408291911e-07, -2.43067969901950e-07, -2.42204118185889e-07, -2.41343838510839e-07,
-2.40487115299025e-07, -2.39633934456146e-07, -2.38784280229563e-07, -2.37938138352777e-07,
-2.37095493714761e-07, -2.36256331764187e-07, -2.35420637665687e-07, -2.34588396605247e-07,
-2.33759594189509e-07, -2.32934215653415e-07, -2.32112246631913e-07, -2.31293672197761e-07,
-2.30478478606337e-07, -2.29666650498245e-07, -2.28858174459892e-07, -2.28053035350143e-07,
-2.27251219550532e-07, -2.26452712188088e-07, -2.25657499664740e-07, -2.24865567423907e-07,
-2.24076901469740e-07, -2.23291487854251e-07, -2.22509312432375e-07, -2.21730361244388e-07,
-2.20954620563434e-07, -2.20182076211984e-07, -2.19412714694147e-07, -2.18646521903486e-07,
-2.17883484383896e-07, -2.17123588353817e-07, -2.16366820128069e-07, -2.15613166183448e-07,
-2.14862613029627e-07, -2.14115146993814e-07, -2.13370754878158e-07, -2.12629423099772e-07,
-2.11891138363819e-07, -2.11155887496477e-07, -2.10423656995905e-07, -2.09694433885185e-07,
-2.08968204970039e-07, -2.08244957067640e-07, -2.07524677166718e-07, -2.06807352224454e-07,
-2.06092969485739e-07, -2.05381515631287e-07, -2.04672978311599e-07, -2.03967344193686e-07,
-2.03264601021340e-07, -2.02564735657223e-07, -2.01867735746392e-07, -2.01173588350793e-07,
-2.00482281305259e-07, -1.99793801823571e-07, -1.99108137387542e-07, -1.98425275805058e-07,
-1.97745204532935e-07, -1.97067911329036e-07, -1.96393383764238e-07, -1.95721610078360e-07,
-1.95052577243684e-07, -1.94386274080193e-07, -1.93722687947528e-07, -1.93061806757312e-07,
-1.92403619005847e-07, -1.91748112297142e-07, -1.91095274888230e-07, -1.90445095092696e-07,
-1.89797560900003e-07, -1.89152660651371e-07, -1.88510382826366e-07, -1.87870715443499e-07,
-1.87233647227950e-07, -1.86599166426662e-07, -1.85967261604676e-07, -1.85337921421058e-07,
-1.84711134173744e-07, -1.84086888956050e-07, -1.83465173928285e-07, -1.82845978411044e-07,
-1.82229290570306e-07, -1.81615099809769e-07, -1.81003394623467e-07, -1.80394164130003e-07,
-1.79787397191637e-07, -1.79183082960416e-07, -1.78581210462729e-07, -1.77981768604749e-07,
-1.77384747010192e-07, -1.76790134329175e-07, -1.76197920279244e-07, -1.75608093946367e-07,
-1.75020644654140e-07, -1.74435562073365e-07, -1.73852835025553e-07, -1.73272453827853e-07,
-1.72694407327890e-07, -1.72118685536102e-07, -1.71545277612669e-07, -1.70974173956787e-07,
-1.70405363526383e-07, -1.69838836363747e-07, -1.69274582612598e-07, -1.68712591481683e-07,
-1.68152853486732e-07, -1.67595358070170e-07, -1.67040095551238e-07, -1.66487055813613e-07,
-1.65936228940280e-07, -1.65387604985621e-07, -1.64841174363218e-07, -1.64296926966630e-07,
-1.63754853189057e-07, -1.63214943277436e-07, -1.62677187786154e-07, -1.62141576630153e-07,
-1.61608100753451e-07, -1.61076750176733e-07, -1.60547515808573e-07, -1.60020387816708e-07,
-1.59495357001039e-07, -1.58972414150008e-07, -1.58451549465726e-07, -1.57932754285846e-07,
-1.57416018767740e-07, -1.56901334211866e-07, -1.56388691080137e-07, -1.55878080602274e-07,
-1.55369493329619e-07, -1.54862920648992e-07, -1.54358353282091e-07, -1.53855782221312e-07,
-1.53355198929552e-07, -1.52856594160304e-07, -1.52359959257812e-07, -1.51865285467035e-07,
-1.51372563950348e-07, -1.50881786077699e-07, -1.50392943026435e-07, -1.49906026536738e-07,
-1.49421027511298e-07, -1.48937937974601e-07, -1.48456748743934e-07, -1.47977452123132e-07,
-1.47500039007716e-07, -1.47024501442303e-07, -1.46550830836957e-07, -1.46079019102679e-07,
-1.45609057558438e-07, -1.45140938613224e-07, -1.44674653350475e-07, -1.44210194290262e-07,
-1.43747552640289e-07, -1.43286720978616e-07, -1.42827690711838e-07, -1.42370454119569e-07,
-1.41915003270239e-07, -1.41461329981941e-07, -1.41009426619173e-07, -1.40559285165464e-07,
-1.40110897804651e-07, -1.39664256855422e-07, -1.39219354451869e-07, -1.38776182998543e-07,
-1.38334734557875e-07, -1.37895001957240e-07, -1.37456976971701e-07, -1.37020652711196e-07,
-1.36586020996076e-07, -1.36153074805632e-07, -1.35721806437522e-07, -1.35292208424720e-07,
-1.34864273706707e-07, -1.34437994360819e-07, -1.34013363619088e-07, -1.33590373843485e-07,
-1.33169017945174e-07, -1.32749288507807e-07, -1.32331178653848e-07, -1.31914680899270e-07,
-1.31499788314931e-07, -1.31086493801924e-07, -1.30674790163481e-07, -1.30264670653015e-07,
-1.29856127931302e-07, -1.29449155358238e-07, -1.29043745755212e-07, -1.28639892510339e-07,
-1.28237588393564e-07, -1.27836826970566e-07, -1.27437601240648e-07, -1.27039904340628e-07,
-1.26643729867720e-07, -1.26249070772313e-07, -1.25855920577385e-07, -1.25464272716693e-07,
-1.25074120297270e-07, -1.24685457156130e-07, -1.24298276313449e-07, -1.23912571661433e-07,
-1.23528336419410e-07, -1.23145564293921e-07, -1.22764248825758e-07, -1.22384383620477e-07,
-1.22005962412361e-07, -1.21628978578079e-07, -1.21253426351929e-07, -1.20879298782689e-07,
-1.20506590361100e-07, -1.20135294215220e-07, -1.19765404706309e-07, -1.19396915179024e-07,
-1.19029820145892e-07, -1.18664112685013e-07, -1.18299787668767e-07, -1.17936838223639e-07,
-1.17575258890661e-07, -1.17215043518218e-07, -1.16856186089489e-07, -1.16498680741125e-07,
-1.16142521638249e-07, -1.15787702900672e-07, -1.15434218467910e-07, -1.15082063045978e-07,
-1.14731230120519e-07, -1.14381714738651e-07, -1.14033510474680e-07, -1.13686612124060e-07,
-1.13341013735002e-07, -1.12996709791271e-07, -1.12653694558815e-07, -1.12311962628278e-07,
-1.11971508286489e-07, -1.11632325933687e-07, -1.11294410375389e-07, -1.10957755681805e-07,
-1.10622356682732e-07, -1.10288208014341e-07, -1.09955303883647e-07, -1.09623639408703e-07,
-1.09293208713016e-07, -1.08964006988832e-07, -1.08636028479464e-07, -1.08309268156813e-07,
-1.07983720692693e-07, -1.07659380897612e-07, -1.07336243438416e-07, -1.07014303306876e-07,
-1.06693555115887e-07, -1.06373994113808e-07, -1.06055614718286e-07, -1.05738412146972e-07,
-1.05422381357636e-07, -1.05107517103486e-07, -1.04793814549719e-07, -1.04481268639380e-07,
-1.04169874348049e-07, -1.03859626965367e-07, -1.03550521269341e-07, -1.03242552438191e-07,
-1.02935715893193e-07, -1.02630006349309e-07, -1.02325419216323e-07, -1.02021949829456e-07,
-1.01719592905307e-07, -1.01418344377258e-07, -1.01118198927787e-07, -1.00819152139622e-07,
-1.00521199132771e-07, -1.00224335644815e-07, -9.99285562939317e-08, -9.96338573379021e-08,
-9.93402334812669e-08, -9.90476803381960e-08, -9.87561936580277e-08, -9.84657684059308e-08,
-9.81764004391603e-08, -9.78880851622638e-08, -9.76008177883101e-08, -9.73145946379674e-08,
-9.70294102354756e-08, -9.67452611863865e-08, -9.64621423413907e-08, -9.61800497145537e-08,
-9.58989788637937e-08, -9.56189254531312e-08, -9.53398852893475e-08, -9.50618537241223e-08,
-9.47848270096250e-08, -9.45088004716146e-08, -9.42337700205555e-08, -9.39597317088125e-08,
-9.36866807695111e-08, -9.34146135724319e-08, -9.31435257575768e-08, -9.28734131930946e-08,
-9.26042717863703e-08, -9.23360973927640e-08, -9.20688860364992e-08, -9.18026336734819e-08,
-9.15373360309584e-08, -9.12729895970861e-08, -9.10095897103722e-08, -9.07471329935015e-08,
-9.04856151907225e-08, -9.02250322774495e-08, -8.99653806269596e-08, -8.97066561221806e-08,
-8.94488548773067e-08, -8.91919732379498e-08, -8.89360069478959e-08, -8.86809527055717e-08,
-8.84268062131136e-08, -8.81735639827318e-08, -8.79212221700109e-08, -8.76697768808299e-08,
-8.74192245544721e-08, -8.71695613455094e-08, -8.69207837698655e-08, -8.66728876268581e-08,
-8.64258698886087e-08, -8.61797264392104e-08, -8.59344538995750e-08, -8.56900483636352e-08,
-8.54465066302882e-08, -8.52038247598642e-08, -8.49619992856401e-08, -8.47210268089180e-08,
-8.44809035190202e-08, -8.42416261859618e-08, -8.40031910012336e-08, -8.37655947795087e-08,
-8.35288338645450e-08, -8.32929047503556e-08, -8.30578042449374e-08, -8.28235286382750e-08,
-8.25900747571734e-08, -8.23574390204138e-08, -8.21256181648958e-08, -8.18946088402252e-08,
-8.16644076160424e-08, -8.14350112470985e-08, -8.12064163827795e-08, -8.09786196867753e-08,
-8.07516179819483e-08, -8.05254078842562e-08, -8.02999862340134e-08, -8.00753496251016e-08,
-7.98514951907328e-08, -7.96284192634520e-08, -7.94061190627864e-08, -7.91845910594019e-08,
-7.89638323891377e-08, -7.87438397192918e-08, -7.85246099269518e-08, -7.83061400737006e-08,
-7.80884267174388e-08, -7.78714671360783e-08, -7.76552580075251e-08, -7.74397962464066e-08,
};

double am_xK1(double x)
{
    unsigned int i, ip;
    double a, b, c, d;
    double u;

    if (x < 0.5) {
        x *= XK1_XSCALE;
        i = (unsigned int)(x);
        ip = i + 1;
        a = (double)ip - x;
        b = 1. - a;
        c = a * a * a - a;
        d = b * b * b - b;
        return a * XK1_y[i] + b * XK1_y[ip] + c * XK1_y2[i] + d * XK1_y2[ip];
    }
    u = XK1_USCALE / x;
    i = (unsigned int)(u);
    ip = i + 1;
    a = (double)ip - u;
    b = 1. - a;
    c = a * a * a - a;
    d = b * b * b - b;
    return a * XK1_v[i] + b * XK1_v[ip] + c * XK1_v2[i] + d * XK1_v2[ip];
}   /* am_xK1() */