/***************************************************************************  **************************************************************************                  Spherical Harmonic Transform Kit 2.7       Contact: Peter Kostelec            geelong@cs.dartmouth.edu       Copyright 1997-2003  Sean Moore, Dennis Healy,                        Dan Rockmore, Peter Kostelec       Copyright 2004  Peter Kostelec, Dan Rockmore     SpharmonicKit is free software; you can redistribute it and/or modify     it under the terms of the GNU General Public License as published by     the Free Software Foundation; either version 2 of the License, or     (at your option) any later version.       SpharmonicKit is distributed in the hope that it will be useful,     but WITHOUT ANY WARRANTY; without even the implied warranty of     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the     GNU General Public License for more details.       You should have received a copy of the GNU General Public License     along with this program; if not, write to the Free Software     Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.       Commercial use is absolutely prohibited.     See the accompanying LICENSE file for details.    ************************************************************************  ************************************************************************//****  OUR supermoduli arrays used in FCTs. See Sean's  thesis for details. The interface function (defined at the  bottom of this file) is  const double *get_mods(int n)  ****/static const double mod2[2] = {-0.7071067811865475, 0.7071067811865475};static const double mod4[4] = {-0.923879532511287, 0.923879532511287, 0.3826834323650897,   -0.3826834323650898};static const double mod8[8] = {-0.98078528040323, 0.98078528040323, 0.1950903220161282,   -0.1950903220161283, -0.5555702330196023, 0.555570233019602,   0.831469612302545, -0.831469612302545};static const double mod16[16] = {-0.995184726672197, 0.995184726672197, 0.0980171403295607,   -0.0980171403295608, -0.6343932841636457, 0.6343932841636453,   0.7730104533627369, -0.773010453362737, -0.881921264348355,   0.881921264348355, 0.4713967368259978, -0.4713967368259978,   -0.2902846772544623, 0.2902846772544622, 0.956940335732209,   -0.956940335732209};static const double mod32[32] ={-0.998795456205172, 0.998795456205172, 0.04906767432741801,   -0.04906767432741814, -0.6715589548470185, 0.6715589548470185,   0.7409511253549589, -0.7409511253549593, -0.903989293123443,   0.903989293123443, 0.4275550934302819, -0.4275550934302822,   -0.33688985339222, 0.3368898533922199, 0.941544065183021,   -0.941544065183021, -0.970031253194544, 0.970031253194544,   0.2429801799032639, -0.242980179903264, -0.5141027441932219,   0.5141027441932216, 0.857728610000272, -0.857728610000272,   -0.803207531480645, 0.803207531480645, 0.5956993044924333,   -0.5956993044924336, -0.1467304744553617, 0.1467304744553616,   0.989176509964781, -0.989176509964781};static const double mod64[64] ={-0.999698818696204, 0.999698818696204, 0.02454122852291214,   -0.02454122852291227, -0.689540544737067, 0.6895405447370669,   0.7242470829514668, -0.7242470829514671, -0.914209755703531,   0.914209755703531, 0.4052413140049898, -0.4052413140049899,   -0.3598950365349883, 0.3598950365349882, 0.932992798834739,   -0.932992798834739, -0.975702130038529, 0.975702130038528,   0.2191012401568697, -0.2191012401568698, -0.5349976198870974,   0.534997619887097, 0.844853565249707, -0.844853565249707,   -0.817584813151584, 0.817584813151584, 0.5758081914178454,   -0.5758081914178455, -0.1709618887603014, 0.1709618887603012,   0.985277642388941, -0.985277642388941, -0.99247953459871, 0.99247953459871,   0.1224106751992162, -0.1224106751992163, -0.6152315905806269,   0.6152315905806267, 0.7883464276266061, -0.7883464276266064,   -0.870086991108711, 0.870086991108711, 0.492898192229784,   -0.4928981922297842, -0.2667127574748984, 0.2667127574748983,   0.96377606579544, -0.96377606579544, -0.949528180593037, 0.949528180593037,   0.3136817403988914, -0.3136817403988915, -0.4496113296546067,   0.4496113296546067, 0.893224301195515, -0.893224301195515,   -0.7572088465064847, 0.7572088465064847, 0.6531728429537766,   -0.6531728429537769, -0.07356456359966746, 0.07356456359966735,   0.99729045667869, -0.99729045667869};static const double mod128[128] ={-0.999924701839145, 0.999924701839145, 0.01227153828571982,   -0.01227153828571994, -0.698376249408973, 0.6983762494089728,   0.7157308252838185, -0.7157308252838188, -0.919113851690058,   0.919113851690058, 0.393992040061048, -0.3939920400610481,   -0.3713171939518376, 0.3713171939518375, 0.928506080473215,   -0.928506080473215, -0.978317370719628, 0.978317370719628,   0.2071113761922184, -0.2071113761922186, -0.5453249884220466,   0.5453249884220462, 0.838224705554838, -0.838224705554838,   -0.824589302785025, 0.824589302785025, 0.5657318107836132,   -0.5657318107836132, -0.183039887955141, 0.1830398879551409,   0.983105487431216, -0.983105487431216, -0.993906970002356,   0.993906970002356, 0.1102222072938831, -0.1102222072938832,   -0.6248594881423865, 0.6248594881423863, 0.7807372285720944,   -0.7807372285720945, -0.876070094195407, 0.876070094195407,   0.4821837720791227, -0.4821837720791229, -0.278519689385053,   0.278519689385053, 0.960430519415566, -0.960430519415566,   -0.953306040354194, 0.953306040354194, 0.3020059493192281,   -0.3020059493192282, -0.4605387109582401, 0.4605387109582402,   0.887639620402854, -0.887639620402854, -0.765167265622459,   0.765167265622459, 0.6438315428897913, -0.6438315428897915,   -0.0857973123444399, 0.0857973123444398, 0.996312612182778,   -0.996312612182778, -0.998118112900149, 0.998118112900149,   0.06132073630220854, -0.06132073630220866, -0.6624157775901719,   0.6624157775901719, 0.7491363945234591, -0.7491363945234594,   -0.898674465693954, 0.898674465693954, 0.4386162385385274,   -0.4386162385385277, -0.325310292162263, 0.3253102921622629,   0.945607325380521, -0.945607325380521, -0.966976471044852,   0.966976471044852, 0.2548656596045145, -0.2548656596045146,   -0.5035383837257176, 0.5035383837257175, 0.863972856121587,   -0.863972856121587, -0.7958369046088836, 0.7958369046088835,   0.6055110414043254, -0.6055110414043256, -0.1345807085071262,   0.1345807085071261, 0.99090263542778, -0.99090263542778,   -0.987301418157858, 0.987301418157858, 0.1588581433338613,   -0.1588581433338614, -0.5857978574564389, 0.5857978574564389,   0.810457198252595, -0.810457198252595, -0.851355193105265,   0.851355193105265, 0.5245896826784687, -0.524589682678469,   -0.2310581082806713, 0.2310581082806711, 0.97293995220556,   -0.97293995220556, -0.937339011912575, 0.937339011912575,   0.3484186802494344, -0.3484186802494345, -0.4164295600976374,   0.416429560097637, 0.909167983090523, -0.909167983090523,   -0.7326542716724129, 0.7326542716724127, 0.6806009977954531,   -0.6806009977954531, -0.03680722294135899, 0.03680722294135887,   0.99932238458835, -0.99932238458835};static const double mod256[256] ={-0.999981175282601, 0.999981175282601, 0.006135884649154394,   -0.006135884649154516, -0.7027547444572254, 0.7027547444572252,   0.7114321957452165, -0.7114321957452165, -0.921514039342042,   0.921514039342042, 0.3883450466988262, -0.3883450466988263,   -0.3770074102164183, 0.3770074102164182, 0.926210242138311,   -0.926210242138311, -0.97956976568544, 0.97956976568544,   0.2011046348420918, -0.2011046348420919, -0.5504579729366049,   0.5504579729366048, 0.83486287498638, -0.83486287498638,   -0.828045045257756, 0.828045045257756, 0.5606615761973359,   -0.5606615761973361, -0.1890686641498063, 0.1890686641498062,   0.981963869109555, -0.981963869109555, -0.994564570734255,   0.994564570734255, 0.1041216338720546, -0.1041216338720547,   -0.6296382389149271, 0.629638238914927, 0.7768884656732322,   -0.7768884656732325, -0.879012226428634, 0.879012226428634,   0.476799230063322, -0.4767992300633223, -0.2844075372112718,   0.2844075372112717, 0.958703474895872, -0.958703474895872,   -0.955141168305771, 0.955141168305771, 0.2961508882436238,   -0.2961508882436239, -0.4659764957679661, 0.465976495767966,   0.884797098430938, -0.884797098430938, -0.7691033376455798,   0.7691033376455795, 0.6391244448637758, -0.6391244448637759,   -0.0919089564971327, 0.0919089564971326, 0.99576741446766,   -0.99576741446766, -0.998475580573295, 0.998475580573295,   0.05519524434968992, -0.05519524434969004, -0.6669999223036376,   0.6669999223036374, 0.7450577854414659, -0.7450577854414661,   -0.901348847046022, 0.901348847046022, 0.433093818853152,   -0.433093818853152, -0.3311063057598764, 0.3311063057598763,   0.94359345816196, -0.94359345816196, -0.968522094274417, 0.968522094274417,   0.2489276057457201, -0.2489276057457203, -0.5088301425431072,   0.5088301425431072, 0.860866938637767, -0.860866938637767,   -0.799537269107905, 0.799537269107905, 0.6006164793838687,   -0.600616479383869, -0.1406582393328492, 0.1406582393328491,   0.990058210262297, -0.990058210262297, -0.988257567730749,   0.988257567730749, 0.1527971852584433, -0.1527971852584434,   -0.5907597018588743, 0.5907597018588741, 0.806847553543799,   -0.806847553543799, -0.8545579883654, 0.8545579883654, 0.5193559901655897,   -0.5193559901655897, -0.2370236059943673, 0.2370236059943672,   0.971503890986252, -0.971503890986252, -0.93945922360219, 0.93945922360219,   0.3426607173119943, -0.3426607173119944, -0.4220002707997998,   0.4220002707997998, 0.906595704514915, -0.906595704514915,   -0.7368165688773699, 0.7368165688773698, 0.6760927035753159,   -0.6760927035753161, -0.04293825693494096, 0.04293825693494084,   0.999077727752645, -0.999077727752645, -0.999529417501093,   0.999529417501093, 0.03067480317663646, -0.03067480317663658,   -0.6850836677727005, 0.6850836677727001, 0.7284643904482252,   -0.7284643904482254, -0.91170603200543, 0.91170603200543,   0.4108431710579038, -0.4108431710579039, -0.3541635254204905,   0.3541635254204904, 0.935183509938948, -0.935183509938948,   -0.974339382785576, 0.974339382785576, 0.2250839113597927,   -0.2250839113597927, -0.5298036246862949, 0.5298036246862946,   0.848120344803297, -0.848120344803297, -0.814036329705948,   0.814036329705948, 0.5808139580957644, -0.5808139580957647,   -0.1649131204899701, 0.1649131204899699, 0.986308097244599,   -0.986308097244599, -0.9917097536691, 0.9917097536691, 0.1284981107937931,   -0.1284981107937932, -0.6103828062763095, 0.6103828062763095,   0.7921065773002122, -0.7921065773002124, -0.867046245515693,   0.867046245515693, 0.4982276669727816, -0.498227666972782,   -0.2607941179152756, 0.2607941179152755, 0.965394441697689,   -0.96539444169769, -0.947585591017741, 0.947585591017741,   0.3195020308160156, -0.3195020308160157, -0.4441221445704293,   0.4441221445704292, 0.895966249756185, -0.895966249756185,   -0.7531867990436126, 0.7531867990436125, 0.6578066932970785,   -0.6578066932970788, -0.06744391956366412, 0.067443919563664,   0.997723066644192, -0.997723066644192, -0.996820299291166,   0.996820299291166, 0.07968243797143002, -0.07968243797143014,   -0.6485144010221126, 0.6485144010221124, 0.7612023854842617,