/* Some constants and matrices that we'll need.
*/
static const double xi[33] = {
-1., -0.99518472667219688624, -0.98078528040323044912,
-0.95694033573220886493, -0.92387953251128675612,
-0.88192126434835502970, -0.83146961230254523708,
-0.77301045336273696082, -0.70710678118654752440,
-0.63439328416364549822, -0.55557023301960222475,
-0.47139673682599764857, -0.38268343236508977173,
-0.29028467725446236764, -0.19509032201612826785,
-0.098017140329560601995, 0., 0.098017140329560601995,
0.19509032201612826785, 0.29028467725446236764, 0.38268343236508977173,
0.47139673682599764857, 0.55557023301960222475, 0.63439328416364549822,
0.70710678118654752440, 0.77301045336273696082, 0.83146961230254523708,
0.88192126434835502970, 0.92387953251128675612, 0.95694033573220886493,
0.98078528040323044912, 0.99518472667219688624, 1.
};
static const double bee[68] = {
0.00000000000000e+00, 2.28868854108532e-01, 0.00000000000000e+00,
-8.15740215243451e-01, 0.00000000000000e+00, 5.31212715259731e-01,
0.00000000000000e+00, 1.38538036812454e-02, 0.00000000000000e+00,
3.74405228908818e-02, 0.00000000000000e+00, 2.12224115039342e-01,
0.00000000000000e+00, -8.16362644507898e-01, 0.00000000000000e+00,
5.35648426691481e-01, 0.00000000000000e+00, 1.52417902753662e-03,
0.00000000000000e+00, 2.63058840550873e-03, 0.00000000000000e+00,
4.15292106318904e-03, 0.00000000000000e+00, 6.97106011119775e-03,
0.00000000000000e+00, 1.35535708431058e-02, 0.00000000000000e+00,
3.52132898424856e-02, 0.00000000000000e+00, 2.06946714741884e-01,
0.00000000000000e+00, -8.15674251283876e-01, 0.00000000000000e+00,
5.38841175520580e-01, 0.00000000000000e+00, 1.84909689577590e-04,
0.00000000000000e+00, 2.90936325007499e-04, 0.00000000000000e+00,
3.84877750950089e-04, 0.00000000000000e+00, 4.86436656735046e-04,
0.00000000000000e+00, 6.08688640346879e-04, 0.00000000000000e+00,
7.66732830740331e-04, 0.00000000000000e+00, 9.82753336104205e-04,
0.00000000000000e+00, 1.29359957505615e-03, 0.00000000000000e+00,
1.76616363801885e-03, 0.00000000000000e+00, 2.53323433039089e-03,
0.00000000000000e+00, 3.88872172121956e-03, 0.00000000000000e+00,
6.58635106468291e-03, 0.00000000000000e+00, 1.30326736343254e-02,
0.00000000000000e+00, 3.44353850696714e-02, 0.00000000000000e+00,
2.05025409531915e-01, 0.00000000000000e+00, -8.14985893995401e-01,
0.00000000000000e+00, 5.40679930965238e-01
};
static const double Lalpha[33] = {
5.77350269189626e-01, 5.16397779494322e-01, 5.07092552837110e-01,
5.03952630678970e-01, 5.02518907629606e-01, 5.01745206004255e-01,
5.01280411827603e-01, 5.00979432868120e-01, 5.00773395667191e-01,
5.00626174321759e-01, 5.00517330712619e-01, 5.00434593736979e-01,
5.00370233297676e-01, 5.00319182924304e-01, 5.00278009473803e-01,
5.00244319584578e-01, 5.00216403386025e-01, 5.00193012939056e-01,
5.00173220168024e-01, 5.00156323280355e-01, 5.00141783641018e-01,
5.00129182278347e-01, 5.00118189340972e-01, 5.00108542278496e-01,
5.00100030010004e-01, 5.00092481273333e-01, 5.00085755939229e-01,
5.00079738458365e-01, 5.00074332862969e-01, 5.00069458915387e-01,
5.00065049112355e-01, 5.00061046334395e-01, 5.00057401986298e-01
};
static const double Lgamma[33] = {
0.0, 0.0, 5.16397779494322e-01, 5.07092552837110e-01, 5.03952630678970e-01,
5.02518907629606e-01, 5.01745206004255e-01, 5.01280411827603e-01,
5.00979432868120e-01, 5.00773395667191e-01, 5.00626174321759e-01,
5.00517330712619e-01, 5.00434593736979e-01, 5.00370233297676e-01,
5.00319182924304e-01, 5.00278009473803e-01, 5.00244319584578e-01,
5.00216403386025e-01, 5.00193012939056e-01, 5.00173220168024e-01,
5.00156323280355e-01, 5.00141783641018e-01, 5.00129182278347e-01,
5.00118189340972e-01, 5.00108542278496e-01, 5.00100030010003e-01,
5.00092481273333e-01, 5.00085755939229e-01, 5.00079738458365e-01,
5.00074332862969e-01, 5.00069458915387e-01, 5.00065049112355e-01,
5.00061046334395e-01
};
static const double V1inv[5 * 5] = {
.47140452079103168293e-1, .37712361663282534635, .56568542494923801952,
.37712361663282534635, .47140452079103168293e-1,
-.81649658092772603273e-1, -.46188021535170061160, 0,
.46188021535170061160, .81649658092772603273e-1, .15058465048420853962,
.12046772038736683169, -.54210474174315074262, .12046772038736683169,
.15058465048420853962, -.21380899352993950775, .30237157840738178177, -0.,
-.30237157840738178177, .21380899352993950775, .10774960475223581324,
-.21549920950447162648, .21549920950447162648, -.21549920950447162648,
.10774960475223581324
};
static const double V2inv[9 * 9] = {
.11223917161691230546e-1, .10339219839658349826, .19754094204576565761,
.25577315077753587922, .27835314560994251755, .25577315077753587922,
.19754094204576565761, .10339219839658349826, .11223917161691230546e-1,
-.19440394783993476970e-1, -.16544884625069155470, -.24193725566041460608,
-.16953338808305493604, 0.0, .16953338808305493604, .24193725566041460608,
.16544884625069155470, .19440394783993476970e-1, .26466393115406349388e-1,
.17766815796285469394, .11316664642449611462, -.16306601003711325980,
-.30847037493128779631, -.16306601003711325980, .11316664642449611462,
.17766815796285469394, .26466393115406349388e-1,
-.32395302049990834508e-1, -.15521142532414866547,
.88573492664788602740e-1, .29570405784974857322, 0.0,
-.29570405784974857322, -.88573492664788602740e-1, .15521142532414866547,
.32395302049990834508e-1, .41442155673936851246e-1,
.98186757907405608245e-1, -.23056908429499411784,
-.68047008326360625520e-1, .31797435808002456774,
-.68047008326360625520e-1, -.23056908429499411784,
.98186757907405608245e-1, .41442155673936851246e-1,
-.49981120317798783134e-1, -.24861810572835756217e-1,
.23561326072010832539, -.24472785656448415351, 0.0, .24472785656448415351,
-.23561326072010832539, .24861810572835756217e-1,
.49981120317798783134e-1, .79691635865674781228e-1,
-.95725617891693941833e-1, -.57957553356854386344e-1,
.21164072460540271452, -.27529837844505833514, .21164072460540271452,
-.57957553356854386344e-1, -.95725617891693941833e-1,
.79691635865674781228e-1,
-.10894869830716590913, .20131094491947531782, -.15407672674888869038,
.83385723639789791384e-1, 0.0, -.83385723639789791384e-1,
.15407672674888869038, -.20131094491947531782, .10894869830716590913,
.54581057089643838221e-1, -.10916211417928767644, .10916211417928767644,
-.10916211417928767644, .10916211417928767644, -.10916211417928767644,
.10916211417928767644, -.10916211417928767644, .54581057089643838221e-1
};
static const double V3inv[17 * 17] = {
.27729677693590098996e-2, .26423663180333065153e-1,
.53374068493933898312e-1, .77007854739523195947e-1,
.98257061072911596869e-1, .11538049741786835604, .12832134344120884559,
.13612785914022865001, .13888293186236181317, .13612785914022865001,
.12832134344120884559, .11538049741786835604, .98257061072911596869e-1,
.77007854739523195947e-1, .53374068493933898312e-1,
.26423663180333065153e-1, .27729677693590098996e-2,
-.48029210642807413690e-2, -.44887724635478800254e-1,
-.85409520147301089416e-1, -.11090267822061423050, -.12033983162705862441,
-.11102786862182788886, -.85054870109799336515e-1,
-.45998467987742225160e-1, 0.0, .45998467987742225160e-1,
.85054870109799336515e-1, .11102786862182788886, .12033983162705862441,
.11090267822061423050, .85409520147301089416e-1, .44887724635478800254e-1,
.48029210642807413690e-2, .62758546879582030087e-2,
.55561297093529155869e-1,
.93281491021051539742e-1, .92320151237493695139e-1,
.55077987469605684531e-1,
-.96998141716497488255e-2, -.80285961895427405567e-1,
-.13496839655913850224,
-.15512521776684524331, -.13496839655913850224, -.80285961895427405567e-1,
-.96998141716497488255e-2, .55077987469605684531e-1,
.92320151237493695139e-1, .93281491021051539742e-1,
.55561297093529155869e-1, .62758546879582030087e-2,
-.74850969394858555939e-2, -.61751608943839234096e-1,
-.82974150437304275958e-1, -.38437763431942633378e-1,
.45745502025779701366e-1, .12369235652734542162, .14720439712852868239,
.98768034347019704401e-1, 0.0,
-.98768034347019704401e-1, -.14720439712852868239, -.12369235652734542162,
-.45745502025779701366e-1, .38437763431942633378e-1,
.82974150437304275958e-1, .61751608943839234096e-1,
.74850969394858555939e-2, .86710099994384056338e-2,
.64006230103659573344e-1, .58517426396091675690e-1,
-.29743410528985802680e-1,
-.11934127779157114754, -.12686773515361299409, -.30729137153877447035e-1,
.97307836256600731568e-1, .15635811574451401023, .97307836256600731568e-1,
-.30729137153877447035e-1, -.12686773515361299409, -.11934127779157114754,
-.29743410528985802680e-1, .58517426396091675690e-1,
.64006230103659573344e-1, .86710099994384056338e-2,
-.97486395666294840165e-2, -.62995604908060224672e-1,
-.24373234450275529219e-1, .87760984413626872730e-1,
.12205204576993351394,
.16216004196864002088e-1, -.12422320942156845775, -.13682714580929614678,
0.0, .13682714580929614678, .12422320942156845775,
-.16216004196864002088e-1, -.12205204576993351394,
-.87760984413626872730e-1, .24373234450275529219e-1,
.62995604908060224672e-1, .97486395666294840165e-2,
.10956271233750488468e-1, .58613204255294358939e-1,
-.13306063940736618859e-1, -.11606666444978454399,
-.52059598001115805639e-1, .10868540217796151849, .12594452879014618005,
-.44678658254872910434e-1, -.15617684362128533405,
-.44678658254872910434e-1, .12594452879014618005, .10868540217796151849,
-.52059598001115805639e-1, -.11606666444978454399,
-.13306063940736618859e-1, .58613204255294358939e-1,
.10956271233750488468e-1, -.12098893000863087230e-1,
-.51626244709126208453e-1, .48919433304746979330e-1,
.10467644465949427090,
-.48729879523084673782e-1, -.13668732103524749234, .28190838706814496438e-1,
.15434223333238741600, 0.0, -.15434223333238741600,
-.28190838706814496438e-1, .13668732103524749234,
.48729879523084673782e-1, -.10467644465949427090,
-.48919433304746979330e-1, .51626244709126208453e-1,
.12098893000863087230e-1, .13542668300437944822e-1,
.41712033418258689308e-1,
-.76190463272803434388e-1, -.58303943170068132010e-1, .12158068748245606853,
.42121099930651007882e-1, -.14684425840766337756,
-.16108203535058647043e-1, .15698075850757976092,
-.16108203535058647043e-1, -.14684425840766337756,
.42121099930651007882e-1, .12158068748245606853,
-.58303943170068132010e-1, -.76190463272803434388e-1,
.41712033418258689308e-1, .13542668300437944822e-1,
-.14939634995117694417e-1, -.30047246373341564039e-1,
.91624635082546425678e-1, -.79133374319110026377e-2,
-.12292558212072233355, .90013382617762643524e-1,
.84013717196539593395e-1, -.14813033309980695856, 0.0,
.14813033309980695856, -.84013717196539593395e-1,
-.90013382617762643524e-1,
.12292558212072233355, .79133374319110026377e-2, -.91624635082546425678e-1,
.30047246373341564039e-1, .14939634995117694417e-1,
.16986031342807474208e-1,
.15760203882617033601e-1, -.91494054040950941996e-1,
.70082459207876130806e-1,
.53390713710144539104e-1, -.14340746778352039430, .84048122493418898508e-1,
.72456667788091316868e-1, -.15564535320096811360,
.72456667788091316868e-1, .84048122493418898508e-1,
-.14340746778352039430, .53390713710144539104e-1,
.70082459207876130806e-1, -.91494054040950941996e-1,
.15760203882617033601e-1,
.16986031342807474208e-1, -.18994065631858742028e-1,
-.82901821370405592927e-3, .77239669773015192888e-1,
-.10850735431039424680, .47524484622086496464e-1,
.69148184871588737021e-1, -.14829314646228194928, .11992057742398672066,
0.0, -.11992057742398672066, .14829314646228194928,
-.69148184871588737021e-1, -.47524484622086496464e-1,
.10850735431039424680, -.77239669773015192888e-1,
.82901821370405592927e-3, .18994065631858742028e-1,
.22761703826371535132e-1, -.17728848711449643358e-1,
-.47496371572480503788e-1, .10659958402328690063, -.11696013966166296514,
.63073750910894244526e-1, .32928881123602721303e-1,
-.12280950532497593683, .15926189077282729505, -.12280950532497593683,
.32928881123602721303e-1, .63073750910894244526e-1,
-.11696013966166296514, .10659958402328690063, -.47496371572480503788e-1,
-.17728848711449643358e-1, .22761703826371535132e-1,
-.26493215276042203434e-1, .35579780856128386192e-1,
.10447309718398935122e-1, -.68616154085314996709e-1,
.11775363082763954214, -.13918901977011837274, .12312819418827395690,
-.72053565748259077905e-1, 0.0, .72053565748259077905e-1,
-.12312819418827395690, .13918901977011837274, -.11775363082763954214,
.68616154085314996709e-1, -.10447309718398935122e-1,
-.35579780856128386192e-1,
.26493215276042203434e-1, .40742523354399706918e-1,
-.73124912999529117195e-1, .49317266444153837821e-1,
-.13686605413876015320e-1, -.28342624942191100464e-1,
.70371855298258216249e-1, -.10600251632853603875, .12981016288391131812,
-.13817029659318161476, .12981016288391131812, -.10600251632853603875,
.70371855298258216249e-1, -.28342624942191100464e-1,
-.13686605413876015320e-1,
.49317266444153837821e-1, -.73124912999529117195e-1,
.40742523354399706918e-1, -.54944368958699908688e-1,
.10777725663147408190, -.10152395581538265428, .91369146312596428468e-1,
-.77703071757424700773e-1, .61050911730999815031e-1,
-.42052599404498348871e-1, .21438229266251454773e-1, 0.0,
-.21438229266251454773e-1, .42052599404498348871e-1,
-.61050911730999815031e-1, .77703071757424700773e-1,
-.91369146312596428468e-1,
.10152395581538265428, -.10777725663147408190, .54944368958699908688e-1,
.27485608464748840573e-1, -.54971216929497681146e-1,
.54971216929497681146e-1,
-.54971216929497681146e-1, .54971216929497681146e-1,
-.54971216929497681146e-1, .54971216929497681146e-1,
-.54971216929497681146e-1, .54971216929497681146e-1,
-.54971216929497681146e-1, .54971216929497681146e-1,
-.54971216929497681146e-1, .54971216929497681146e-1,
-.54971216929497681146e-1, .54971216929497681146e-1,
-.54971216929497681146e-1, .27485608464748840573e-1
};
static const double V4inv[33 * 33] = {
.69120897476690862600e-3, .66419939766331555194e-2,
.13600665164323186111e-1, .20122785860913684493e-1,
.26583214101668429944e-1, .32712713318999268739e-1,
.38576221976287138036e-1, .44033030938268925133e-1,
.49092709529622799673e-1, .53657949874312515646e-1,
.57724533144734311859e-1, .61219564530655179096e-1,
.64138907503837875026e-1, .66427905189318792009e-1,
.68088956652280022887e-1, .69083051391555695878e-1,
.69422738116739271449e-1, .69083051391555695878e-1,
.68088956652280022887e-1, .66427905189318792009e-1,
.64138907503837875026e-1, .61219564530655179096e-1,
.57724533144734311859e-1, .53657949874312515646e-1,
.49092709529622799673e-1, .44033030938268925133e-1,
.38576221976287138036e-1, .32712713318999268739e-1,
.26583214101668429944e-1, .20122785860913684493e-1,
.13600665164323186111e-1, .66419939766331555194e-2,
.69120897476690862600e-3, -.11972090629438798134e-2,
-.11448874821643225573e-1, -.23104401104002905904e-1,
-.33352899418646530133e-1, -.42538626424075425908e-1,
-.49969730733911825941e-1, -.55555454015360728353e-1,
-.58955533624852604918e-1, -.60126044219122513907e-1,
-.58959430451175833624e-1, -.55546925396227130606e-1,
-.49984739749347973762e-1, -.42513009141170294365e-1,
-.33399140950669746346e-1, -.23007690803851790829e-1,
-.11728275717520066169e-1, 0.0, .11728275717520066169e-1,
.23007690803851790829e-1, .33399140950669746346e-1,
.42513009141170294365e-1, .49984739749347973762e-1,
.55546925396227130606e-1, .58959430451175833624e-1,
.60126044219122513907e-1, .58955533624852604918e-1,
.55555454015360728353e-1, .49969730733911825941e-1,
.42538626424075425908e-1, .33352899418646530133e-1,
.23104401104002905904e-1, .11448874821643225573e-1,
.11972090629438798134e-2, .15501585012936019146e-2,
.14628781502199620482e-1, .28684915921474815271e-1,
.39299396074628048026e-1, .46393418975496284204e-1,
.48756902531094699526e-1, .46331333488337494692e-1,
.39012645376980228775e-1, .27452795421085791153e-1,
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static const double Tleft[33 * 33] = {
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