quadcc.cc

Go to the documentation of this file.

/*

Copyright (C) 2010-2013 Pedro Gonnet

This file is part of Octave.

Octave 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 3 of the License, or (at your
option) any later version.

Octave 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 Octave; see the file COPYING.  If not, see
<http://www.gnu.org/licenses/>.

*/

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include "lo-ieee.h"
#include "parse.h"
#include "variables.h"

#include "defun.h"
#include "error.h"
#include "oct-obj.h"
#include "utils.h"


/* Extended debugging */
#define DEBUG_QUADCC 0

/* Define the minimum size of the interval heap. */
#define min_cquad_heapsize  200


/* Data of a single interval */
typedef struct
{
  double a, b;
  double c[64];
  double fx[33];
  double igral, err;
  int depth, rdepth, ndiv;
} cquad_ival;

/* 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,
  .12430953621169863781e-1, -.47682978056024928800e-2,
  -.22825828045428973853e-1,
  -.40195512090720278312e-1, -.55503004262826221955e-1,
  -.67424537752827046308e-1, -.75020199300113606452e-1,
  -.77607844312483656131e-1, -.75020199300113606452e-1,
  -.67424537752827046308e-1, -.55503004262826221955e-1,
  -.40195512090720278312e-1, -.22825828045428973853e-1,
  -.47682978056024928800e-2, .12430953621169863781e-1,
  .27452795421085791153e-1, .39012645376980228775e-1,
  .46331333488337494692e-1, .48756902531094699526e-1,
  .46393418975496284204e-1, .39299396074628048026e-1,
  .28684915921474815271e-1, .14628781502199620482e-1,
  .15501585012936019146e-2, -.18377757558949194214e-2,
  -.17050470050949761565e-1, -.31952119564923250836e-1,
  -.40197423449026348155e-1,
  -.41205649520281371624e-1, -.33909965817492272248e-1,
  -.19393664422115332144e-1, .56661049630886784692e-3,
  .22948272173686561721e-1, .44489719570904738207e-1,
  .61790363672287920596e-1, .72121014727028013894e-1,
  .73627151185287858579e-1, .65784665375961398923e-1,
  .49369676372333667559e-1, .26444326317059715065e-1, 0.0,
  -.26444326317059715065e-1, -.49369676372333667559e-1,
  -.65784665375961398923e-1, -.73627151185287858579e-1,
  -.72121014727028013894e-1, -.61790363672287920596e-1,
  -.44489719570904738207e-1, -.22948272173686561721e-1,
  -.56661049630886784692e-3, .19393664422115332144e-1,
  .33909965817492272248e-1, .41205649520281371624e-1,
  .40197423449026348155e-1, .31952119564923250836e-1,
  .17050470050949761565e-1, .18377757558949194214e-2,
  .20942714740729767769e-2, .18935902405146518232e-1,
  .33335840852491735126e-1, .36770680999102286065e-1,
  .28873194534132768509e-1, .10267303017729535513e-1,
  -.14607738306201572890e-1, -.40139568545572305818e-1,
  -.59808326733858291561e-1, -.68528358823372627506e-1,
  -.63306535387619244879e-1, -.44508601817574921056e-1,
  -.15449116105605395357e-1, .17941083795006546367e-1,
  .48747356011657242123e-1, .70329553984201665523e-1,
  .78106117292526169663e-1, .70329553984201665523e-1,
  .48747356011657242123e-1, .17941083795006546367e-1,
  -.15449116105605395357e-1, -.44508601817574921056e-1,
  -.63306535387619244879e-1, -.68528358823372627506e-1,
  -.59808326733858291561e-1,
  -.40139568545572305818e-1, -.14607738306201572890e-1,
  .10267303017729535513e-1, .28873194534132768509e-1,
  .36770680999102286065e-1, .33335840852491735126e-1,
  .18935902405146518232e-1, .20942714740729767769e-2,
  -.23245285491878278419e-2, -.20401404737639389919e-1,
  -.33019548231022514097e-1, -.29709828426463720091e-1,
  -.11760070922697422156e-1, .15987584743850393793e-1,
  .43619012891472813485e-1, .61177322409671487721e-1,
  .61144030218486655594e-1,
  .41895377620089086167e-1, .80232011820644308033e-2,
  -.30574701186675900915e-1,
  -.62072243008844865848e-1, -.76336186183574765586e-1,
  -.68435466095345537115e-1, -.40237669208466966207e-1, 0.0,
  .40237669208466966207e-1, .68435466095345537115e-1,
  .76336186183574765586e-1, .62072243008844865848e-1,
  .30574701186675900915e-1, -.80232011820644308033e-2,
  -.41895377620089086167e-1, -.61144030218486655594e-1,
  -.61177322409671487721e-1, -.43619012891472813485e-1,
  -.15987584743850393793e-1, .11760070922697422156e-1,
  .29709828426463720091e-1, .33019548231022514097e-1,
  .20401404737639389919e-1, .23245285491878278419e-2,
  .25451717261579269307e-2, .21480418595666878775e-1,
  .31177212469293007998e-1, .19816333607013379373e-1,
  -.72439496274458793681e-2, -.38404203906598342397e-1,
  -.57633632255322221046e-1, -.54070547403585392952e-1,
  -.26249823354368866005e-1, .15643058212336881516e-1,
  .54539832735118677194e-1, .73283028002473989724e-1,
  .62835303524135936213e-1, .26175977027801048141e-1,
  -.22193636309998606610e-1, -.62597049956093311234e-1,
  -.78206986173170212505e-1, -.62597049956093311234e-1,
  -.22193636309998606610e-1, .26175977027801048141e-1,
  .62835303524135936213e-1,
  .73283028002473989724e-1, .54539832735118677194e-1,
  .15643058212336881516e-1,
  -.26249823354368866005e-1, -.54070547403585392952e-1,
  -.57633632255322221046e-1, -.38404203906598342397e-1,
  -.72439496274458793681e-2, .19816333607013379373e-1,
  .31177212469293007998e-1, .21480418595666878775e-1,
  .25451717261579269307e-2, -.27506573922483820005e-2,
  -.22224442095099251870e-1, -.27949927254215773020e-1,
  -.80918481053370034987e-2, .25121859354449306916e-1,
  .51563535009373061074e-1, .51936965107145960512e-1,
  .22146626648171527753e-1,
  -.24172689882103382748e-1, -.61731229104853568296e-1,
  -.68477262429344201201e-1, -.38311232728303704742e-1,
  .14160578713659552679e-1, .61248813427564184033e-1,
  .77136328841293031805e-1, .52514801765183697988e-1, 0.0,
  -.52514801765183697988e-1, -.77136328841293031805e-1,
  -.61248813427564184033e-1, -.14160578713659552679e-1,
  .38311232728303704742e-1,
  .68477262429344201201e-1, .61731229104853568296e-1,
  .24172689882103382748e-1,
  -.22146626648171527753e-1, -.51936965107145960512e-1,
  -.51563535009373061074e-1, -.25121859354449306916e-1,
  .80918481053370034987e-2, .27949927254215773020e-1,
  .22224442095099251870e-1, .27506573922483820005e-2,
  .29562461131654311467e-2, .22630271480554450613e-1,
  .23547399831373800971e-1, -.43964593440902476642e-2,
  -.39055315767504970597e-1, -.52369643937940066804e-1,
  -.28506131614971613422e-1, .19906048093338832322e-1,
  .60408880866392420279e-1, .62493397473656883090e-1,
  .21391278377641297859e-1, -.37302864786623254746e-1,
  -.73665127933539496872e-1, -.61706142476854010202e-1,
  -.78065168882546327888e-2, .52335307373945544428e-1,
  .78278746279419264777e-1, .52335307373945544428e-1,
  -.78065168882546327888e-2, -.61706142476854010202e-1,
  -.73665127933539496872e-1, -.37302864786623254746e-1,
  .21391278377641297859e-1, .62493397473656883090e-1,
  .60408880866392420279e-1, .19906048093338832322e-1,
  -.28506131614971613422e-1, -.52369643937940066804e-1,
  -.39055315767504970597e-1, -.43964593440902476642e-2,
  .23547399831373800971e-1, .22630271480554450613e-1,
  .29562461131654311467e-2, -.31515718415504761303e-2,
  -.22739451096655080673e-1, -.18157123602272119779e-1,
  .16496480897167303621e-1, .46921166788569301124e-1,
  .40644395739978416354e-1, -.46275803430732216900e-2,
  -.52883375891308909486e-1, -.61116483226324111734e-1,
  -.17411698764545629853e-1, .44773430013166822765e-1,
  .73441577962383869198e-1, .42127368371995472815e-1,
  -.25504645957196772465e-1, -.74126818045972742488e-1,
  -.62780077864719287317e-1, 0.0, .62780077864719287317e-1,
  .74126818045972742488e-1, .25504645957196772465e-1,
  -.42127368371995472815e-1, -.73441577962383869198e-1,
  -.44773430013166822765e-1, .17411698764545629853e-1,
  .61116483226324111734e-1, .52883375891308909486e-1,
  .46275803430732216900e-2, -.40644395739978416354e-1,
  -.46921166788569301124e-1, -.16496480897167303621e-1,
  .18157123602272119779e-1, .22739451096655080673e-1,
  .31515718415504761303e-2, .33536559294882188208e-2,
  .22535348942792006185e-1,
  .12048629300953560767e-1, -.27166076791299493403e-1,
  -.47492745604230978367e-1, -.19246623430993153174e-1,
  .36231297307556299322e-1, .61713617181636122004e-1,
  .25928029734266134490e-1, -.40478700752883602818e-1,
  -.71053889866326412049e-1, -.31870824482961751482e-1,
  .41515251100219081281e-1, .76481960760098381651e-1,
  .36726509155999912440e-1, -.40090067032627055969e-1,
  -.78270742903374539397e-1, -.40090067032627055969e-1,
  .36726509155999912440e-1, .76481960760098381651e-1,
  .41515251100219081281e-1, -.31870824482961751482e-1,
  -.71053889866326412049e-1, -.40478700752883602818e-1,
  .25928029734266134490e-1, .61713617181636122004e-1,
  .36231297307556299322e-1, -.19246623430993153174e-1,
  -.47492745604230978367e-1, -.27166076791299493403e-1,
  .12048629300953560767e-1, .22535348942792006185e-1,
  .33536559294882188208e-2,
  -.35481220456925318865e-2, -.22062913693073191150e-1,
  -.54487362861834144999e-2, .35438821865804087489e-1,
  .40733077820527411302e-1, -.67403098138950720914e-2,
  -.55559584405239171054e-1, -.42417050790865158745e-1,
  .24499901971884704925e-1, .68721232891705409302e-1,
  .34086082787461126592e-1, -.43441000373118474002e-1,
  -.73878085292669148950e-1, -.18846995664706657127e-1,
  .59827776178286834498e-1, .70644634584085901794e-1, 0.0,
  -.70644634584085901794e-1, -.59827776178286834498e-1,
  .18846995664706657127e-1, .73878085292669148950e-1,
  .43441000373118474002e-1, -.34086082787461126592e-1,
  -.68721232891705409302e-1, -.24499901971884704925e-1,
  .42417050790865158745e-1, .55559584405239171054e-1,
  .67403098138950720914e-2, -.40733077820527411302e-1,
  -.35438821865804087489e-1, .54487362861834144999e-2,
  .22062913693073191150e-1, .35481220456925318865e-2,
  .37554176816665075631e-2, .21297045781589919482e-1,
  -.13327293083183431816e-2,
  -.40635299172764596484e-1, -.27659860508374175359e-1,
  .31089232744083445986e-1, .56113781541334176109e-1,
  .37577840643257763400e-2, -.60511227350664590865e-1,
  -.46670556446129053853e-1, .33263195878575888247e-1,
  .72757324720645228775e-1, .15011712351692283635e-1,
  -.65601212994924119078e-1, -.60016855838843789772e-1,
  .26220858553188665966e-1, .78322776605833552980e-1,
  .26220858553188665966e-1, -.60016855838843789772e-1,
  -.65601212994924119078e-1,
  .15011712351692283635e-1, .72757324720645228775e-1,
  .33263195878575888247e-1,
  -.46670556446129053853e-1, -.60511227350664590865e-1,
  .37577840643257763400e-2, .56113781541334176109e-1,
  .31089232744083445986e-1, -.27659860508374175359e-1,
  -.40635299172764596484e-1, -.13327293083183431816e-2,
  .21297045781589919482e-1, .37554176816665075631e-2,
  -.39566995305720591229e-2, -.20291873414438919995e-1,
  .80617453830770930551e-2, .42270189157016547906e-1,
  .10332624526759093004e-1, -.48054759547616142024e-1,
  -.37678032941171643972e-1,
  .36617192625732482394e-1, .61009425973424865714e-1,
  -.95589113168026591466e-2,
  -.71023202645076922361e-1, -.25097788086808784456e-1,
  .62406621963267050244e-1, .56907293171100693511e-1,
  -.36435383083882206257e-1, -.75790105119208756348e-1, 0.0,
  .75790105119208756348e-1, .36435383083882206257e-1,
  -.56907293171100693511e-1, -.62406621963267050244e-1,
  .25097788086808784456e-1, .71023202645076922361e-1,
  .95589113168026591466e-2,
  -.61009425973424865714e-1, -.36617192625732482394e-1,
  .37678032941171643972e-1, .48054759547616142024e-1,
  -.10332624526759093004e-1, -.42270189157016547906e-1,
  -.80617453830770930551e-2, .20291873414438919995e-1,
  .39566995305720591229e-2, .41776092289182138591e-2,
  .19013221163904414395e-1, -.14420609729849899876e-1,
  -.40259160586844441220e-1, .86327811113710831649e-2,
  .53564430703021034399e-1, .65469185402150431933e-2,
  -.60383116311280629856e-1,
  -.25657793784058876939e-1, .58745680576829226900e-1,
  .45649937869034420296e-1,
  -.49167932056844167772e-1, -.62696614328552187977e-1,
  .32540234556426699997e-1, .74280410383464269758e-1,
  -.11425672633410999870e-1, -.78280649404686404903e-1,
  -.11425672633410999870e-1, .74280410383464269758e-1,
  .32540234556426699997e-1, -.62696614328552187977e-1,
  -.49167932056844167772e-1, .45649937869034420296e-1,
  .58745680576829226900e-1, -.25657793784058876939e-1,
  -.60383116311280629856e-1, .65469185402150431933e-2,
  .53564430703021034399e-1,
  .86327811113710831649e-2, -.40259160586844441220e-1,
  -.14420609729849899876e-1, .19013221163904414395e-1,
  .41776092289182138591e-2, -.43935502082478059199e-2,
  -.17528761237509401631e-1, .20208915249153872535e-1,
  .34734743119040669109e-1, -.26275910172353637955e-1,
  -.46368003346018878786e-1,
  .26800056330709381025e-1, .56681476464606609921e-1,
  -.24749011438127255898e-1,
  -.64934612189056658992e-1, .20333742247679279535e-1,
  .71429299070059318651e-1,
  -.14452513210428671266e-1, -.75793341281736586582e-1,
  .74717094137184935270e-2, .78034921554757317374e-1, 0.0,
  -.78034921554757317374e-1, -.74717094137184935270e-2,
  .75793341281736586582e-1, .14452513210428671266e-1,
  -.71429299070059318651e-1, -.20333742247679279535e-1,
  .64934612189056658992e-1, .24749011438127255898e-1,
  -.56681476464606609921e-1,
  -.26800056330709381025e-1, .46368003346018878786e-1,
  .26275910172353637955e-1,
  -.34734743119040669109e-1, -.20208915249153872535e-1,
  .17528761237509401631e-1, .43935502082478059199e-2,
  .46379089482818671473e-2, .15791188144791287229e-1,
  -.25134290048737455284e-1, -.26249795071946841205e-1,
  .39960457575789924651e-1, .28111892450146525404e-1,
  -.51026476400767918226e-1,
  -.27266747278681831364e-1, .60708796647861610865e-1,
  .23532306960642115854e-1,
  -.68169639871532441111e-1, -.18204924701958312032e-1,
  .73822890510656128485e-1, .11373392486424717019e-1,
  -.77133324017644609416e-1, -.39295877480342619961e-2,
  .78351902829418987960e-1, -.39295877480342619961e-2,
  -.77133324017644609416e-1, .11373392486424717019e-1,
  .73822890510656128485e-1, -.18204924701958312032e-1,
  -.68169639871532441111e-1, .23532306960642115854e-1,
  .60708796647861610865e-1, -.27266747278681831364e-1,
  -.51026476400767918226e-1, .28111892450146525404e-1,
  .39960457575789924651e-1, -.26249795071946841205e-1,
  -.25134290048737455284e-1, .15791188144791287229e-1,
  .46379089482818671473e-2, -.48780095920069827068e-2,
  -.13886961667516983541e-1, .29071311049368895844e-1,
  .15480559452075811600e-1, -.47527977686242313065e-1,
  -.31929089844361042178e-2, .58015667638415922967e-1,
  -.14547915466597622925e-1, -.61067668299848923244e-1,
  .35093678009090186851e-1, .55378399159800654657e-1,
  -.54277226474891610385e-1, -.42023830782434076509e-1,
  .69197384645944912066e-1, .22610783557709586445e-1,
  -.77269275900637030185e-1, 0.0, .77269275900637030185e-1,
  -.22610783557709586445e-1,
  -.69197384645944912066e-1, .42023830782434076509e-1,
  .54277226474891610385e-1,
  -.55378399159800654657e-1, -.35093678009090186851e-1,
  .61067668299848923244e-1, .14547915466597622925e-1,
  -.58015667638415922967e-1, .31929089844361042178e-2,
  .47527977686242313065e-1, -.15480559452075811600e-1,
  -.29071311049368895844e-1, .13886961667516983541e-1,
  .48780095920069827068e-2, .51591759101720291381e-2,
  .11747497650231330965e-1, -.31777863364694653331e-1,
  -.34555825499804605557e-2, .47914131921157015198e-1,
  -.22573685920142225247e-1, -.45320344390022666738e-1,
  .49660630547172186418e-1, .25707858143963615736e-1,
  -.68132707341917233933e-1, .67534860185243140399e-2,
  .69268150370037450063e-1, -.41585011920451477177e-1,
  -.51622397460510041271e-1, .68408139576363036148e-1,
  .18981259024768933323e-1, -.78265472429342305554e-1,
  .18981259024768933323e-1, .68408139576363036148e-1,
  -.51622397460510041271e-1,
  -.41585011920451477177e-1, .69268150370037450063e-1,
  .67534860185243140399e-2,
  -.68132707341917233933e-1, .25707858143963615736e-1,
  .49660630547172186418e-1,
  -.45320344390022666738e-1, -.22573685920142225247e-1,
  .47914131921157015198e-1, -.34555825499804605557e-2,
  -.31777863364694653331e-1, .11747497650231330965e-1,
  .51591759101720291381e-2, -.54365757412741340377e-2,
  -.94862516619529080191e-2, .33240472093448190877e-1,
  -.88698898099681552229e-2,
  -.40973252097216337576e-1, .42995673349795657065e-1,
  .17320914507876958783e-1,
  -.62201292691914856803e-1, .24726274174637346693e-1,
  .51320859246515407288e-1,
  -.62882063373810501763e-1, -.11003569131725622672e-1,
  .73842261324108943465e-1, -.39240120294802923208e-1,
  -.49293966443941122807e-1, .73552644778818223475e-1, 0.0,
  -.73552644778818223475e-1, .49293966443941122807e-1,
  .39240120294802923208e-1, -.73842261324108943465e-1,
  .11003569131725622672e-1, .62882063373810501763e-1,
  -.51320859246515407288e-1,
  -.24726274174637346693e-1, .62201292691914856803e-1,
  -.17320914507876958783e-1, -.42995673349795657065e-1,
  .40973252097216337576e-1, .88698898099681552229e-2,
  -.33240472093448190877e-1, .94862516619529080191e-2,
  .54365757412741340377e-2, .57750194549356126240e-2,
  .69981166020044116791e-2, -.33274982140403110792e-1,
  .20297071020698356116e-1, .27898517839646066582e-1,
  -.53368678853282030262e-1, .16656482990394548343e-1,
  .46342901447260614255e-1,
  -.60536796508149003365e-1, .29109107483842596340e-2,
  .63224486124385124504e-1,
  -.59028872851312033411e-1, -.14783105962696191734e-1,
  .74269399241069253865e-1, -.49053677339382384625e-1,
  -.33525466624811186739e-1, .78397349622515386647e-1,
  -.33525466624811186739e-1, -.49053677339382384625e-1,
  .74269399241069253865e-1, -.14783105962696191734e-1,
  -.59028872851312033411e-1,
  .63224486124385124504e-1, .29109107483842596340e-2,
  -.60536796508149003365e-1,
  .46342901447260614255e-1, .16656482990394548343e-1,
  -.53368678853282030262e-1,
  .27898517839646066582e-1, .20297071020698356116e-1,
  -.33274982140403110792e-1,
  .69981166020044116791e-2, .57750194549356126240e-2,
  -.61100308370519200637e-2, -.44383614355738148616e-2,
  .32011283412619094811e-1, -.29965011866372897633e-1,
  -.10560682331349193348e-1, .51110336443392506342e-1,
  -.45012284729681775492e-1, -.94236825555873320102e-2,
  .60860695783141264746e-1,
  -.55014628647083368926e-1, -.73474782382499482121e-2,
  .66640148475243034781e-1, -.62533116045749887988e-1,
  -.38650525912400102585e-2, .68429769005837003777e-1,
  -.66984505412544901945e-1, 0.0, .66984505412544901945e-1,
  -.68429769005837003777e-1, .38650525912400102585e-2,
  .62533116045749887988e-1, -.66640148475243034781e-1,
  .73474782382499482121e-2,
  .55014628647083368926e-1, -.60860695783141264746e-1,
  .94236825555873320102e-2,
  .45012284729681775492e-1, -.51110336443392506342e-1,
  .10560682331349193348e-1,
  .29965011866372897633e-1, -.32011283412619094811e-1,
  .44383614355738148616e-2,
  .61100308370519200637e-2, .65409373892036191538e-2,
  .16350101107071157065e-2, -.29301957285983144319e-1,
  .36838667173388832579e-1, -.81922703976491586393e-2,
  -.36955670021050133434e-1, .58374851095540469865e-1,
  -.31977016246946181856e-1, -.25311073698658094646e-1,
  .66674413950106952577e-1,
  -.54865713324521039571e-1, -.39797027891537985440e-2,
  .62830285264808449064e-1, -.72226313251296100676e-1,
  .22560232697133353980e-1, .46455784709904033738e-1,
  -.78200930751070349956e-1, .46455784709904033738e-1,
  .22560232697133353980e-1, -.72226313251296100676e-1,
  .62830285264808449064e-1, -.39797027891537985440e-2,
  -.54865713324521039571e-1, .66674413950106952577e-1,
  -.25311073698658094646e-1, -.31977016246946181856e-1,
  .58374851095540469865e-1, -.36955670021050133434e-1,
  -.81922703976491586393e-2, .36838667173388832579e-1,
  -.29301957285983144319e-1, .16350101107071157065e-2,
  .65409373892036191538e-2, -.69686180931868703196e-2,
  .11849538727632789870e-2, .25452286414610537766e-1,
  -.40522480651713943230e-1, .25694679053362813183e-1,
  .14057118113748390637e-1, -.52037614725803488893e-1,
  .58849342223684035589e-1,
  -.25075229077361409271e-1, -.29559771094034181083e-1,
  .68296746944165720199e-1, -.62890462146423984955e-1,
  .14457636466274596445e-1, .45787612031322361496e-1,
  -.77231759014655809742e-1, .57881203613910543657e-1, 0.0,
  -.57881203613910543657e-1, .77231759014655809742e-1,
  -.45787612031322361496e-1, -.14457636466274596445e-1,
  .62890462146423984955e-1,
  -.68296746944165720199e-1, .29559771094034181083e-1,
  .25075229077361409271e-1,
  -.58849342223684035589e-1, .52037614725803488893e-1,
  -.14057118113748390637e-1, -.25694679053362813183e-1,
  .40522480651713943230e-1, -.25452286414610537766e-1,
  -.11849538727632789870e-2, .69686180931868703196e-2,
  .75611653617520254845e-2, -.43290610418608409141e-2,
  -.20277062025115566914e-1,
  .40362947027704828926e-1, -.38938808024132120254e-1,
  .11831186195916702262e-1,
  .28476667401744525357e-1, -.59320969056617684621e-1,
  .61101629747436200186e-1,
  -.29514834848355389223e-1, -.20668001885001084821e-1,
  .62923592802445122793e-1, -.73558456263588833115e-1,
  .45314556330160999776e-1, .79031645918426015574e-2,
  -.58136953576334689357e-1, .78538474524006405758e-1,
  -.58136953576334689357e-1, .79031645918426015574e-2,
  .45314556330160999776e-1, -.73558456263588833115e-1,
  .62923592802445122793e-1, -.20668001885001084821e-1,
  -.29514834848355389223e-1, .61101629747436200186e-1,
  -.59320969056617684621e-1, .28476667401744525357e-1,
  .11831186195916702262e-1, -.38938808024132120254e-1,
  .40362947027704828926e-1, -.20277062025115566914e-1,
  -.43290610418608409141e-2, .75611653617520254845e-2,
  -.81505692478987769484e-2, .74297333588288568430e-2,
  .14314212513540223314e-1, -.36711242251332751607e-1,
  .46240027755503814626e-1, -.34921532671769023773e-1,
  .46930051972353714773e-2,
  .32842770336385381562e-1, -.61317813706529588466e-1,
  .67000809902468893103e-1,
  -.45337449655535622885e-1, .35794459576271920867e-2,
  .41830061526027213385e-1,
  -.72091371931944711708e-1, .74150028530317793195e-1,
  -.46487632538609942002e-1, 0.0, .46487632538609942002e-1,
  -.74150028530317793195e-1, .72091371931944711708e-1,
  -.41830061526027213385e-1, -.35794459576271920867e-2,
  .45337449655535622885e-1, -.67000809902468893103e-1,
  .61317813706529588466e-1, -.32842770336385381562e-1,
  -.46930051972353714773e-2, .34921532671769023773e-1,
  -.46240027755503814626e-1, .36711242251332751607e-1,
  -.14314212513540223314e-1, -.74297333588288568430e-2,
  .81505692478987769484e-2, .90693182942442189743e-2,
  -.11121000903959576737e-1, -.71308296141317458546e-2,
  .29219439765986671645e-1, -.45820286629778129593e-1,
  .49088381175879124421e-1, -.35614888785023038938e-1,
  .78906970900092777895e-2,
  .26262843038404929480e-1, -.56143674270125757857e-1,
  .71700220472378350694e-1,
  -.66963544500697307945e-1, .42215091779892228883e-1,
  -.41338867413966866997e-2, -.36164891772995367321e-1,
  .66584367783847858225e-1, -.77874712365070098328e-1,
  .66584367783847858225e-1, -.36164891772995367321e-1,
  -.41338867413966866997e-2, .42215091779892228883e-1,
  -.66963544500697307945e-1,
  .71700220472378350694e-1, -.56143674270125757857e-1,
  .26262843038404929480e-1,
  .78906970900092777895e-2, -.35614888785023038938e-1,
  .49088381175879124421e-1,
  -.45820286629778129593e-1, .29219439765986671645e-1,
  -.71308296141317458546e-2, -.11121000903959576737e-1,
  .90693182942442189743e-2, -.99848472706332791043e-2,
  .14701271465939718856e-1, -.32917820356048383366e-3,
  -.19201195309873585230e-1, .38409681836626963278e-1,
  -.51647324405878909521e-1, .54522171113149311354e-1,
  -.45040302741689006270e-1, .24183738595685990149e-1,
  .42204134165479735097e-2, -.34317295181348742251e-1,
  .59542472465494579941e-1, -.74135115907618101263e-1,
  .74491937840566532596e-1, -.60042604725161994304e-1,
  .33437677409000083169e-1, 0.0,
  -.33437677409000083169e-1, .60042604725161994304e-1,
  -.74491937840566532596e-1, .74135115907618101263e-1,
  -.59542472465494579941e-1, .34317295181348742251e-1,
  -.42204134165479735097e-2, -.24183738595685990149e-1,
  .45040302741689006270e-1, -.54522171113149311354e-1,
  .51647324405878909521e-1, -.38409681836626963278e-1,
  .19201195309873585230e-1, .32917820356048383366e-3,
  -.14701271465939718856e-1, .99848472706332791043e-2,
  .11775579274769383373e-1, -.19892153937316935880e-1,
  .95335114477449041055e-2, .57661528440359081617e-2,
  -.23382690532380910781e-1, .40237257037170725321e-1,
  -.53280289903551636474e-1, .59974361806023689068e-1,
  -.58701684061992853224e-1, .49033407111597129616e-1,
  -.31818835267847249219e-1, .90800541261162098886e-2,
  .16272906819312603838e-1, -.40863896581186229487e-1,
  .61346046297517367703e-1,
  -.74896047554167268919e-1, .79632642148310325817e-1,
  -.74896047554167268919e-1, .61346046297517367703e-1,
  -.40863896581186229487e-1, .16272906819312603838e-1,
  .90800541261162098886e-2, -.31818835267847249219e-1,
  .49033407111597129616e-1, -.58701684061992853224e-1,
  .59974361806023689068e-1, -.53280289903551636474e-1,
  .40237257037170725321e-1, -.23382690532380910781e-1,
  .57661528440359081617e-2, .95335114477449041055e-2,
  -.19892153937316935880e-1,
  .11775579274769383373e-1, -.13562702617218467450e-1,
  .24885419969649845849e-1, -.18368693901908875583e-1,
  .81673147806084084638e-2, .47890591326129587131e-2,
  -.19313752945227974024e-1, .34065953398362954708e-1,
  -.47667045133463415672e-1, .58820377816690514309e-1,
  -.66424139824618415970e-1,
  .69667606260856092515e-1, -.68102459384364543253e-1,
  .61683024923302547971e-1,
  -.50771943476441639136e-1, .36110771847327189215e-1,
  -.18758028464284563358e-1, 0.0, .18758028464284563358e-1,
  -.36110771847327189215e-1, .50771943476441639136e-1,
  -.61683024923302547971e-1, .68102459384364543253e-1,
  -.69667606260856092515e-1, .66424139824618415970e-1,
  -.58820377816690514309e-1, .47667045133463415672e-1,
  -.34065953398362954708e-1, .19313752945227974024e-1,
  -.47890591326129587131e-2, -.81673147806084084638e-2,
  .18368693901908875583e-1, -.24885419969649845849e-1,
  .13562702617218467450e-1, .20576545037980523979e-1,
  -.40093155172981004337e-1, .36954083167944054826e-1,
  -.31856506837591907746e-1, .24996323181546255126e-1,
  -.16637165210473614136e-1, .71002706773325085237e-2,
  .32478629093205201133e-2,
  -.14009562579050569518e-1, .24771262248780618922e-1,
  -.35119395835433647559e-1, .44656290368574753171e-1,
  -.53015448339647394161e-1, .59875631995693046782e-1,
  -.64973208326045193862e-1, .68112280331082143373e-1,
  -.69172215234062186994e-1, .68112280331082143373e-1,
  -.64973208326045193862e-1, .59875631995693046782e-1,
  -.53015448339647394161e-1, .44656290368574753171e-1,
  -.35119395835433647559e-1, .24771262248780618922e-1,
  -.14009562579050569518e-1, .32478629093205201133e-2,
  .71002706773325085237e-2, -.16637165210473614136e-1,
  .24996323181546255126e-1, -.31856506837591907746e-1,
  .36954083167944054826e-1, -.40093155172981004337e-1,
  .20576545037980523979e-1, -.27584914609096156163e-1,
  .54904171411058497973e-1, -.54109756419563083153e-1,
  .52794234894345577483e-1, -.50970276026831042415e-1,
  .48655445537990983379e-1,
  -.45872036510847994332e-1, .42646854695899611372e-1,
  -.39010960357087507670e-1, .34999369144476467749e-1,
  -.30650714874402762189e-1, .26006877464703437057e-1,
  -.21112579608213651273e-1, .16014956068786763273e-1,
  -.10763099747751940252e-1, .54075888924374485533e-2, 0.0,
  -.54075888924374485533e-2, .10763099747751940252e-1,
  -.16014956068786763273e-1,
  .21112579608213651273e-1, -.26006877464703437057e-1,
  .30650714874402762189e-1,
  -.34999369144476467749e-1, .39010960357087507670e-1,
  -.42646854695899611372e-1, .45872036510847994332e-1,
  -.48655445537990983379e-1, .50970276026831042415e-1,
  -.52794234894345577483e-1, .54109756419563083153e-1,
  -.54904171411058497973e-1, .27584914609096156163e-1,
  .13794141262469565740e-1, -.27588282524939131481e-1,
  .27588282524939131481e-1, -.27588282524939131481e-1,
  .27588282524939131481e-1, -.27588282524939131481e-1,
  .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .27588282524939131481e-1,
  -.27588282524939131481e-1, .13794141262469565740e-1
};

static const double Tleft[33 * 33] =
{
  1., -.86602540378443864678, 0., .33071891388307382381, 0.,
  -.20728904939721249057, 0., .15128841196122722208, 0.,
  -.11918864298744029244, 0., .98352013661686631224e-1, 0.,
  -.83727065404940845733e-1, 0., .72893399403505841203e-1, 0.,
  -.64544632643375022436e-1, 0., .57913170372415565639e-1, 0.,
  -.52518242575729562263e-1, 0., .48043311993977520457e-1, 0.,
  -.44271433659733990243e-1, 0., .41048928022856771981e-1, 0.,
  -.38263878662008271459e-1, 0., .35832844026365304501e-1, 0., 0.,
  .50000000000000000000, -.96824583655185422130, .57282196186948000082,
  .21650635094610966169, -.35903516540862679125, -.97578093724974971969e-1,
  .26203921611325660506, .55792409597991015609e-1, -.20644078533943456204,
  -.36172381205961199479e-1, .17035068468874958194,
  .25371838001497225980e-1, -.14501953125000000000,
  -.18786835250972344757e-1, .12625507130328301066,
  .14473795929590520582e-1, -.11179458309419422675,
  -.11494434254897626155e-1, .10030855351241635862,
  .93498556820544479096e-2, -.90964264465390582629e-1,
  -.77546391824364392762e-2, .83213457337452292745e-1,
  .65358085945588638605e-2, -.76680372422574234569e-1,
  -.55835321940047427169e-2, .71098828931825789428e-1,
  .48253327982967591019e-2, -.66274981937248958553e-1,
  -.42118078245337801387e-2, .62064306433355646267e-1,
  .37083386598903548973e-2, 0., 0., .25000000000000000000,
  -.73950997288745200531, .83852549156242113615, -.23175620272173946716,
  -.37791833195149451496, .25710129174850522325, .21608307321780204633,
  -.22844049245646009157, -.14009503000335388415, .19897685605518413847,
  .98264706042471226893e-1, -.17445445004279014046,
  -.72761100054958328401e-1, .15463589893742108388,
  .56056770591708784481e-1, -.13855313872640495158,
  -.44517752443294564781e-1, .12534277657695128850,
  .36211835346039665762e-1, -.11434398255136139683,
  -.30033588409423828125e-1, .10506705408753910481,
  .25313077840725783008e-1, -.97149327637744872155e-1,
  -.21624927200393328444e-1, .90319582367202122625e-1,
  .18688433567711780666e-1, -.84372291635345108584e-1,
  -.16312261561845420752e-1, .79149526894804751586e-1,
  .14362333871852474757e-1, 0., 0., 0., .12500000000000000000,
  -.49607837082461073572, .82265291131801144317, -.59621200088559103072,
  -.80054302859059362371e-1, .42612156697795759420,
  -.90098145270865592887e-1, -.29769623255090078484, .13630307904779758221,
  .21638835185708931831, -.14600247270306082052, -.16348801804014290453,
  .14340708728599057249, .12755243353979286190, -.13661523715071346961,
  -.10215585947881057394, .12864248070157166547, .83592528025348693602e-1,
  -.12066728689302565222, -.69633728678718053052e-1, .11314245177331919532,
  .58882939251410088028e-1, -.10621835858758221487,
  -.50432266865187597572e-1, .99916834723527771581e-1,
  .43672094283057258509e-1, -.94206380251950852413e-1,
  -.38181356812697746418e-1, .89035739656537771225e-1,
  .33661934598216332678e-1, 0., 0., 0., 0., .62500000000000000000e-1,
  -.31093357409581873586, .67604086414949799246, -.75644205980613611039,
  .28990586430124175741, .30648508196770360914, -.35801372616842500052,
  -.91326869828709014708e-1, .31127929687500000000,
  -.90915752838698393094e-2, -.25637381283965534330,
  .57601077850322797594e-1, .21019685709225757945,
  -.81244992138514014256e-1, -.17375078516720988858,
  .92289437277967051125e-1, .14527351914265391374,
  -.96675340792832019889e-1, -.12289485697108543415,
  .97448175340011084006e-1, .10511755943298339844,
  -.96242247086378239657e-1, -.90822942272780513537e-1,
  .93966350452322132384e-1, .79189411876493712558e-1,
  -.91139307067989309325e-1, -.69613039934383197265e-1,
  .88062491671135767870e-1, .61646331729340817494e-1, 0., 0., 0., 0., 0.,
  .31250000000000000000e-1, -.18684782411095934408, .50176689760410660236,
  -.74784031498626095398, .56472001151566251186, .14842464993721351203e-1,
  -.41162920273003120936, .20243071230196532282, .23772054897172750436,
  -.24963810923972235950, -.12116179938394678936, .24330535483519110663,
  .47903849781124471359e-1, -.22133299683101224293,
  -.20542915138527200983e-2, .19653465717678146728,
  -.26818172626509178444e-1, -.17319122357631210944,
  .45065391411065545445e-1, .15253391395444065941,
  -.56543897711725408302e-1, -.13469154928743585367,
  .63632471400208840155e-1, .11941684923913523817,
  -.67828850207933293098e-1, -.10636309084510652670,
  .70095786922999181504e-1, .95187373095150709082e-1, 0., 0., 0., 0., 0.,
  0., .15625000000000000000e-1, -.10909562534194485289,
  .34842348626527747318, -.64461114561628111443, .69382480527334683659,
  -.29551102358528827763, -.25527584713978439819, .38878771718544715394,
  -.82956185835347407489e-2, -.31183177761966943912, .12831420840372374767,
  .22067618205599434368, -.17569196937129496961, -.14598057000132284135,
  .18864406621763419484, .89921002550386645767e-1, -.18571835020187122114,
  -.48967672227195481777e-1, .17584685670380332798,
  .19267984545067426324e-1, -.16335437520503462738,
  .22598055455032407594e-2, .15032800884170631129,
  -.17883358353754640871e-1, -.13774837869432209951,
  .29227555960587143675e-1, .12604194747513151053, 0., 0., 0., 0., 0., 0.,
  0., .78125000000000000000e-2, -.62377810244809812496e-1,
  .23080781467370883845, -.50841310636012325368, .69834547012574056043,
  -.52572723156526459672, .11464215704954976471e-1, .38698869011491210342,
  -.26125646622255207507, -.16951698812361607510, .29773875898928782269,
  .20130501202570367491e-1, -.26332493149159310198,
  .67734613690401207009e-1, .21207315477103762715, -.11541543390889415193,
  -.16249634759782417533, .13885887405041735068, .11996491328010275427,
  -.14810432001630926895, -.85177658352556243411e-1, .14918860659904380587,
  .57317789510444151564e-1, -.14569827645586660151,
  -.35213090145965327390e-1, .13975998126844578198, 0., 0., 0., 0., 0., 0.,
  0., 0., .39062500000000000000e-2, -.35101954600803571207e-1,
  .14761284084133737720, -.37655033076080192966, .62410290231517322776,
  -.64335622317683389875, .28188168266139524244, .22488495672137010675,
  -.39393811089283576186, .75184777995770096714e-1, .28472023119398293003,
  -.20410910833705899572, -.15590046962908511750, .23814567544617953125,
  .54442805556829031204e-1, -.22855930338589720954,
  .16303223615756629897e-1, .20172722433875559213,
  -.62723406421217419404e-1, -.17012230831020922010,
  .91754642766136561612e-1, .13927644821381121197, -.10886600968068418181,
  -.11139075654373395292, .11797455976331702879, 0., 0., 0., 0., 0., 0., 0.,
  0., 0., .19531250000000000000e-2, -.19506820659607596598e-1,
  .91865676095362231937e-1, -.26604607809696493849, .51425874205091288223,
  -.66047561132505329292, .48660109511591303851, -.17575661168678285615e-1,
  -.36594333408055703366, .29088854695378694533, .11318677346656537927,
  -.31110645235730182168, .60733219161008787341e-1, .24333848233620420826,
  -.15254312332655419708, -.15995968483455388613, .19010344455215289289,
  .86040636766440260000e-1, -.19652589954665259945,
  -.27633388517205837713e-1, .18660848552712880387,
  -.15942583868416775867e-1, -.16902042462382064786,
  .47278526495327740646e-1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  .97656250000000000000e-3, -.10731084460857378207e-1,
  .55939644713816406331e-1, -.18118487371914493668, .39914857299829864263,
  -.60812322949933902435, .60011887183061967583, -.26002695805835928795,
  -.20883922404786010096, .38988130966114638081, -.11797833550782589082,
  -.25231824756239520077, .24817859972953934712, .90516417677868996417e-1,
  -.26079073291293066798, .30259468817169480161e-1, .22178195264114178432,
  -.10569877864302048175, -.16679648389266977455, .14637718550245050850,
  .11219272032739559870, -.16359363640525750353, -.64358194509092101393e-1,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .48828125000000000000e-3,
  -.58542865274813470967e-2, .33461741635290096452e-1,
  -.11979993155896201271, .29580223766987206958, -.51874761979436016742,
  .62861483498014306968, -.44868895761051453296, .12567502628371529386e-1,
  .35040366183235474275, -.30466868455569500886, -.70903913601490112666e-1,
  .30822791893032512740, -.11969443264190207736, -.20764760317621313946,
  .20629838355452128532, .95269702915334718507e-1, -.22432624768705133300,
  -.33103381593477797101e-2, .20570036048155716333,
  -.62208282720094518964e-1, -.17095309330441436348, 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., .24414062500000000000e-3,
  -.31714797501871532475e-2, .19721062526127334100e-1,
  -.77311181185536498246e-1, .21124871792841566575, -.41777980401893650886,
  .59401977834943551650, -.56132417807488349048, .23433675061367565951,
  .20222775295220942126, -.38280372496506190127, .14443804214023095767,
  .22268950939178466797, -.27211314150777981984, -.34184876506180717313e-1,
  .26006498895669734842, -.97650425186005090107e-1, -.19024527660129101293,
  .16789164198044635671, .10875811641651905252, -.19276785058805921298, 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .12207031250000000000e-3,
  -.17078941137247586143e-2, .11477733754843910060e-1,
  -.48887017020924625462e-1, .14634927241421789683, -.32156282683019547854,
  .52165811920227223937, -.60001958466396926460, .41208501541480733755,
  -.11366945503190350975e-2, -.33968093962672089159, .30955190935923386766,
  .40657421856578262210e-1, -.29873400409871531764, .16094481791768257440,
  .16876122436206497694, -.23650217045022161255, -.33070260090574765012e-1,
  .22985258456375907796, -.68645651043827097771e-1, 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., .61035156250000000000e-4,
  -.91501857608428649078e-3, .66085179496951987952e-2,
  -.30383171695850355404e-1, .98840838845366876117e-1,
  -.23855447246420318989, .43322017468145613917, -.58049033744876107191,
  .52533893203742699346, -.20681056202371946180, -.20180000924562504384,
  .37503922291962681797, -.15988102869837429062, -.19823558102762374094,
  .28393023878803799622, -.11188133439357510403e-1, -.24730368377168229255,
  .14731529061377942839, .14878558042884266021, 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., .30517578125000000000e-4,
  -.48804277318479845551e-3, .37696080990601968396e-2,
  -.18603912108994738255e-1, .65325006755649582964e-1,
  -.17162960707938819795, .34411527956476971322, -.52289350347082497959,
  .57319653625674910592, -.37662253421045430413, -.14099055105384663902e-1,
  .33265570610216904208, -.30921265572647566661, -.19911390594166455281e-1,
  .28738590811031797718, -.18912130469738472647, -.13235936203215819193,
  .25076406142356675279, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., .15258789062500000000e-4, -.25928719280954633249e-3,
  .21327398937568540428e-2, -.11244626133630732010e-1,
  .42375605740664331966e-1, -.12031130345907846211, .26352562258934426830,
  -.44590628258512682078, .56682835613700749379, -.49116715128261660395,
  .17845943097110339078, .20541650677432497477, -.36739803642257458221,
  .16776034069210108273, .17920950989905112908, -.28867732805385066532,
  .46473465543376206337e-1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., .76293945312500000000e-5, -.13727610943181290891e-3,
  .11979683091449349286e-2, -.67195313034570709806e-2,
  .27044920779931968175e-1, -.82472196498517457862e-1,
  .19570475044896150093, -.36391620788543817693, .52241392782736588032,
  -.54727504974907879912, .34211551468813581183, .31580472732719957762e-1,
  -.32830006549176759667, .30563797665254420769, .64905014620683140120e-2,
  -.27642986248995073032, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., .38146972656250000000e-5,
  -.72454147007837596854e-4, .66859847582761390285e-3,
  -.39751311980366118437e-2, .17015198650201528366e-1,
  -.55443621868993855715e-1, .14157060481641692131, -.28641242619559616836,
  .45610665490966615415, -.55262786406029265394, .45818352706035500108,
  -.14984403004611673047, -.21163807462970713245, .36007252928843413718,
  -.17030961385712954159, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., .19073486328125000000e-5,
  -.38135049864067468562e-4, .37101393638555730015e-3,
  -.23305339886279723213e-2, .10569913448297127219e-1,
  -.36640175162216897547e-1, .10010476414320235508, -.21860074212675559892,
  .38124757096345313719, -.52020999209879669177, .52172632730659212045,
  -.30841620620308814614, -.50322546186721500184e-1, .32577618885114899053,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., .95367431640625000000e-6, -.20021483206955925244e-4,
  .20481807322420625431e-3, -.13553476938058909882e-2,
  .64919676350791905019e-2, -.23848725425069251903e-1,
  .69384632678886421292e-1, -.16249711393618776934, .30736618106830314788,
  -.46399909601971539157, .53765031034002467225, -.42598991476520183929,
  .12130445348350215652, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., .47683715820312500000e-6,
  -.10487707828484902486e-4, .11254146162337528943e-3,
  -.78248929534271987118e-3, .39468337145306794566e-2,
  -.15313546659475671763e-1, .47249070825218564146e-1,
  -.11804374107101480543, .24031796927792491122, -.39629215049166341285,
  .51629108968402548545, -.49622372075429782915, 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  .23841857910156250000e-6, -.54823314130625337326e-5,
  .61575377321535518154e-4, -.44877834366497538134e-3,
  .23774612048621955857e-2, -.97136347645161687796e-2,
  .31671599547606636717e-1, -.84028665767000747480e-1,
  .18298487576742964949, -.32647878537696945218, .46970971486488895077, 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., .11920928955078125000e-6, -.28604020001177375838e-5,
  .33559227978295551013e-4, -.25583821662860610560e-3,
  .14201552747787302339e-2, -.60938046986874414969e-2,
  .20930869247951926793e-1, -.58745021125678072911e-1,
  .13613725780285953720, -.26083988356030237586, 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  .59604644775390625000e-7, -.14898180663526043291e-5,
  .18224991282807693921e-4, -.14504433444608833821e-3,
  .84184722720281809548e-3, -.37846965430000478789e-2,
  .13656355548211376864e-1, -.40409541997718853934e-1,
  .99226988101858325902e-1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  .29802322387695312500e-7, -.77471708843445529468e-6,
  .98649879372606876995e-5, -.81814934772838523887e-4,
  .49554483992403011328e-3, -.23290922072351413938e-2,
  .88068134250844034186e-2, -.27393666952485719070e-1, 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., .14901161193847656250e-7, -.40226235946098233685e-6,
  .53236418690561306700e-5, -.45933829691164002269e-4,
  .28982005232838857913e-3, -.14212974043211018374e-2,
  .56192363087488842264e-2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  .74505805969238281250e-8, -.20858299254133430408e-6,
  .28648457300134381744e-5, -.25677535898258910850e-4,
  .16849420429491355445e-3, -.86062824010315834002e-3, 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., .37252902984619140625e-8, -.10801736017613096861e-6,
  .15376606719887104015e-5, -.14296523739727437959e-4,
  .97419023656050887203e-4, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  .18626451492309570312e-8, -.55871592916438890146e-7,
  .82331193828137454068e-6, -.79302250528382787666e-5, 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., .93132257461547851562e-9,
  -.28867244235852488244e-7, .43982811713864556957e-6, 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., .46566128730773925781e-9,
  -.14899342093408253335e-7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., .23283064365386962891e-9
};

static const double Tright[33 * 33] =
{
  1., .86602540378443864678, 0., -.33071891388307382381, 0.,
  .20728904939721249057, 0., -.15128841196122722208, 0.,
  .11918864298744029244, 0., -.98352013661686631224e-1, 0.,
  .83727065404940845733e-1, 0., -.72893399403505841203e-1, 0.,
  .64544632643375022436e-1, 0., -.57913170372415565639e-1, 0.,
  .52518242575729562263e-1, 0., -.48043311993977520457e-1, 0.,
  .44271433659733990243e-1, 0., -.41048928022856771981e-1, 0.,
  .38263878662008271459e-1, 0., -.35832844026365304501e-1, 0., 0.,
  .50000000000000000000, .96824583655185422130, .57282196186948000082,
  -.21650635094610966169, -.35903516540862679125, .97578093724974971969e-1,
  .26203921611325660506, -.55792409597991015609e-1, -.20644078533943456204,
  .36172381205961199479e-1, .17035068468874958194,
  -.25371838001497225980e-1, -.14501953125000000000,
  .18786835250972344757e-1, .12625507130328301066,
  -.14473795929590520582e-1, -.11179458309419422675,
  .11494434254897626155e-1, .10030855351241635862,
  -.93498556820544479096e-2, -.90964264465390582629e-1,
  .77546391824364392762e-2, .83213457337452292745e-1,
  -.65358085945588638605e-2, -.76680372422574234569e-1,
  .55835321940047427169e-2, .71098828931825789428e-1,
  -.48253327982967591019e-2, -.66274981937248958553e-1,
  .42118078245337801387e-2, .62064306433355646267e-1,
  -.37083386598903548973e-2, 0., 0., .25000000000000000000,
  .73950997288745200531, .83852549156242113615, .23175620272173946716,
  -.37791833195149451496, -.25710129174850522325, .21608307321780204633,
  .22844049245646009157, -.14009503000335388415, -.19897685605518413847,
  .98264706042471226893e-1, .17445445004279014046,
  -.72761100054958328401e-1, -.15463589893742108388,
  .56056770591708784481e-1, .13855313872640495158,
  -.44517752443294564781e-1, -.12534277657695128850,
  .36211835346039665762e-1, .11434398255136139683,
  -.30033588409423828125e-1, -.10506705408753910481,
  .25313077840725783008e-1, .97149327637744872155e-1,
  -.21624927200393328444e-1, -.90319582367202122625e-1,
  .18688433567711780666e-1, .84372291635345108584e-1,
  -.16312261561845420752e-1, -.79149526894804751586e-1,
  .14362333871852474757e-1, 0., 0., 0., .12500000000000000000,
  .49607837082461073572, .82265291131801144317, .59621200088559103072,
  -.80054302859059362371e-1, -.42612156697795759420,
  -.90098145270865592887e-1, .29769623255090078484, .13630307904779758221,
  -.21638835185708931831, -.14600247270306082052, .16348801804014290453,
  .14340708728599057249, -.12755243353979286190, -.13661523715071346961,
  .10215585947881057394, .12864248070157166547, -.83592528025348693602e-1,
  -.12066728689302565222, .69633728678718053052e-1, .11314245177331919532,
  -.58882939251410088028e-1, -.10621835858758221487,
  .50432266865187597572e-1, .99916834723527771581e-1,
  -.43672094283057258509e-1, -.94206380251950852413e-1,
  .38181356812697746418e-1, .89035739656537771225e-1,
  -.33661934598216332678e-1, 0., 0., 0., 0., .62500000000000000000e-1,
  .31093357409581873586, .67604086414949799246, .75644205980613611039,
  .28990586430124175741, -.30648508196770360914, -.35801372616842500052,
  .91326869828709014708e-1, .31127929687500000000, .90915752838698393094e-2,
  -.25637381283965534330, -.57601077850322797594e-1, .21019685709225757945,
  .81244992138514014256e-1, -.17375078516720988858,
  -.92289437277967051125e-1, .14527351914265391374,
  .96675340792832019889e-1, -.12289485697108543415,
  -.97448175340011084006e-1, .10511755943298339844,
  .96242247086378239657e-1, -.90822942272780513537e-1,
  -.93966350452322132384e-1, .79189411876493712558e-1,
  .91139307067989309325e-1, -.69613039934383197265e-1,
  -.88062491671135767870e-1, .61646331729340817494e-1, 0., 0., 0., 0., 0.,
  .31250000000000000000e-1, .18684782411095934408, .50176689760410660236,
  .74784031498626095398, .56472001151566251186, -.14842464993721351203e-1,
  -.41162920273003120936, -.20243071230196532282, .23772054897172750436,
  .24963810923972235950, -.12116179938394678936, -.24330535483519110663,
  .47903849781124471359e-1, .22133299683101224293,
  -.20542915138527200983e-2, -.19653465717678146728,
  -.26818172626509178444e-1, .17319122357631210944,
  .45065391411065545445e-1, -.15253391395444065941,
  -.56543897711725408302e-1, .13469154928743585367,
  .63632471400208840155e-1, -.11941684923913523817,
  -.67828850207933293098e-1, .10636309084510652670,
  .70095786922999181504e-1, -.95187373095150709082e-1, 0., 0., 0., 0., 0.,
  0., .15625000000000000000e-1, .10909562534194485289,
  .34842348626527747318, .64461114561628111443, .69382480527334683659,
  .29551102358528827763, -.25527584713978439819, -.38878771718544715394,
  -.82956185835347407489e-2, .31183177761966943912, .12831420840372374767,
  -.22067618205599434368, -.17569196937129496961, .14598057000132284135,
  .18864406621763419484, -.89921002550386645767e-1, -.18571835020187122114,
  .48967672227195481777e-1, .17584685670380332798,
  -.19267984545067426324e-1, -.16335437520503462738,
  -.22598055455032407594e-2, .15032800884170631129,
  .17883358353754640871e-1, -.13774837869432209951,
  -.29227555960587143675e-1, .12604194747513151053, 0., 0., 0., 0., 0., 0.,
  0., .78125000000000000000e-2, .62377810244809812496e-1,
  .23080781467370883845, .50841310636012325368, .69834547012574056043,
  .52572723156526459672, .11464215704954976471e-1, -.38698869011491210342,
  -.26125646622255207507, .16951698812361607510, .29773875898928782269,
  -.20130501202570367491e-1, -.26332493149159310198,
  -.67734613690401207009e-1, .21207315477103762715, .11541543390889415193,
  -.16249634759782417533, -.13885887405041735068, .11996491328010275427,
  .14810432001630926895, -.85177658352556243411e-1, -.14918860659904380587,
  .57317789510444151564e-1, .14569827645586660151,
  -.35213090145965327390e-1, -.13975998126844578198, 0., 0., 0., 0., 0., 0.,
  0., 0., .39062500000000000000e-2, .35101954600803571207e-1,
  .14761284084133737720, .37655033076080192966, .62410290231517322776,
  .64335622317683389875, .28188168266139524244, -.22488495672137010675,
  -.39393811089283576186, -.75184777995770096714e-1, .28472023119398293003,
  .20410910833705899572, -.15590046962908511750, -.23814567544617953125,
  .54442805556829031204e-1, .22855930338589720954, .16303223615756629897e-1,
  -.20172722433875559213, -.62723406421217419404e-1, .17012230831020922010,
  .91754642766136561612e-1, -.13927644821381121197, -.10886600968068418181,
  .11139075654373395292, .11797455976331702879, 0., 0., 0., 0., 0., 0., 0.,
  0., 0., .19531250000000000000e-2, .19506820659607596598e-1,
  .91865676095362231937e-1, .26604607809696493849, .51425874205091288223,
  .66047561132505329292, .48660109511591303851, .17575661168678285615e-1,
  -.36594333408055703366, -.29088854695378694533, .11318677346656537927,
  .31110645235730182168, .60733219161008787341e-1, -.24333848233620420826,
  -.15254312332655419708, .15995968483455388613, .19010344455215289289,
  -.86040636766440260000e-1, -.19652589954665259945,
  .27633388517205837713e-1, .18660848552712880387, .15942583868416775867e-1,
  -.16902042462382064786, -.47278526495327740646e-1, 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., .97656250000000000000e-3, .10731084460857378207e-1,
  .55939644713816406331e-1, .18118487371914493668, .39914857299829864263,
  .60812322949933902435, .60011887183061967583, .26002695805835928795,
  -.20883922404786010096, -.38988130966114638081, -.11797833550782589082,
  .25231824756239520077, .24817859972953934712, -.90516417677868996417e-1,
  -.26079073291293066798, -.30259468817169480161e-1, .22178195264114178432,
  .10569877864302048175, -.16679648389266977455, -.14637718550245050850,
  .11219272032739559870, .16359363640525750353, -.64358194509092101393e-1,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .48828125000000000000e-3,
  .58542865274813470967e-2, .33461741635290096452e-1, .11979993155896201271,
  .29580223766987206958, .51874761979436016742, .62861483498014306968,
  .44868895761051453296, .12567502628371529386e-1, -.35040366183235474275,
  -.30466868455569500886, .70903913601490112666e-1, .30822791893032512740,
  .11969443264190207736, -.20764760317621313946, -.20629838355452128532,
  .95269702915334718507e-1, .22432624768705133300,
  -.33103381593477797101e-2, -.20570036048155716333,
  -.62208282720094518964e-1, .17095309330441436348, 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., .24414062500000000000e-3,
  .31714797501871532475e-2, .19721062526127334100e-1,
  .77311181185536498246e-1, .21124871792841566575, .41777980401893650886,
  .59401977834943551650, .56132417807488349048, .23433675061367565951,
  -.20222775295220942126, -.38280372496506190127, -.14443804214023095767,
  .22268950939178466797, .27211314150777981984, -.34184876506180717313e-1,
  -.26006498895669734842, -.97650425186005090107e-1, .19024527660129101293,
  .16789164198044635671, -.10875811641651905252, -.19276785058805921298, 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .12207031250000000000e-3,
  .17078941137247586143e-2, .11477733754843910060e-1,
  .48887017020924625462e-1, .14634927241421789683, .32156282683019547854,
  .52165811920227223937, .60001958466396926460, .41208501541480733755,
  .11366945503190350975e-2, -.33968093962672089159, -.30955190935923386766,
  .40657421856578262210e-1, .29873400409871531764, .16094481791768257440,
  -.16876122436206497694, -.23650217045022161255, .33070260090574765012e-1,
  .22985258456375907796, .68645651043827097771e-1, 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., .61035156250000000000e-4,
  .91501857608428649078e-3, .66085179496951987952e-2,
  .30383171695850355404e-1, .98840838845366876117e-1, .23855447246420318989,
  .43322017468145613917, .58049033744876107191, .52533893203742699346,
  .20681056202371946180, -.20180000924562504384, -.37503922291962681797,
  -.15988102869837429062, .19823558102762374094, .28393023878803799622,
  .11188133439357510403e-1, -.24730368377168229255, -.14731529061377942839,
  .14878558042884266021, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., .30517578125000000000e-4, .48804277318479845551e-3,
  .37696080990601968396e-2, .18603912108994738255e-1,
  .65325006755649582964e-1, .17162960707938819795, .34411527956476971322,
  .52289350347082497959, .57319653625674910592, .37662253421045430413,
  -.14099055105384663902e-1, -.33265570610216904208, -.30921265572647566661,
  .19911390594166455281e-1, .28738590811031797718, .18912130469738472647,
  -.13235936203215819193, -.25076406142356675279, 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .15258789062500000000e-4,
  .25928719280954633249e-3, .21327398937568540428e-2,
  .11244626133630732010e-1, .42375605740664331966e-1, .12031130345907846211,
  .26352562258934426830, .44590628258512682078, .56682835613700749379,
  .49116715128261660395, .17845943097110339078, -.20541650677432497477,
  -.36739803642257458221, -.16776034069210108273, .17920950989905112908,
  .28867732805385066532, .46473465543376206337e-1, 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .76293945312500000000e-5,
  .13727610943181290891e-3, .11979683091449349286e-2,
  .67195313034570709806e-2, .27044920779931968175e-1,
  .82472196498517457862e-1, .19570475044896150093, .36391620788543817693,
  .52241392782736588032, .54727504974907879912, .34211551468813581183,
  -.31580472732719957762e-1, -.32830006549176759667, -.30563797665254420769,
  .64905014620683140120e-2, .27642986248995073032, 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .38146972656250000000e-5,
  .72454147007837596854e-4, .66859847582761390285e-3,
  .39751311980366118437e-2, .17015198650201528366e-1,
  .55443621868993855715e-1, .14157060481641692131, .28641242619559616836,
  .45610665490966615415, .55262786406029265394, .45818352706035500108,
  .14984403004611673047, -.21163807462970713245, -.36007252928843413718,
  -.17030961385712954159, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., .19073486328125000000e-5,
  .38135049864067468562e-4, .37101393638555730015e-3,
  .23305339886279723213e-2, .10569913448297127219e-1,
  .36640175162216897547e-1, .10010476414320235508, .21860074212675559892,
  .38124757096345313719, .52020999209879669177, .52172632730659212045,
  .30841620620308814614, -.50322546186721500184e-1, -.32577618885114899053,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., .95367431640625000000e-6, .20021483206955925244e-4,
  .20481807322420625431e-3, .13553476938058909882e-2,
  .64919676350791905019e-2, .23848725425069251903e-1,
  .69384632678886421292e-1, .16249711393618776934, .30736618106830314788,
  .46399909601971539157, .53765031034002467225, .42598991476520183929,
  .12130445348350215652, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., .47683715820312500000e-6,
  .10487707828484902486e-4, .11254146162337528943e-3,
  .78248929534271987118e-3, .39468337145306794566e-2,
  .15313546659475671763e-1, .47249070825218564146e-1, .11804374107101480543,
  .24031796927792491122, .39629215049166341285, .51629108968402548545,
  .49622372075429782915, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., .23841857910156250000e-6,
  .54823314130625337326e-5, .61575377321535518154e-4,
  .44877834366497538134e-3, .23774612048621955857e-2,
  .97136347645161687796e-2, .31671599547606636717e-1,
  .84028665767000747480e-1, .18298487576742964949, .32647878537696945218,
  .46970971486488895077, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .11920928955078125000e-6,
  .28604020001177375838e-5, .33559227978295551013e-4,
  .25583821662860610560e-3, .14201552747787302339e-2,
  .60938046986874414969e-2, .20930869247951926793e-1,
  .58745021125678072911e-1, .13613725780285953720, .26083988356030237586,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., .59604644775390625000e-7,
  .14898180663526043291e-5, .18224991282807693921e-4,
  .14504433444608833821e-3, .84184722720281809548e-3,
  .37846965430000478789e-2, .13656355548211376864e-1,
  .40409541997718853934e-1, .99226988101858325902e-1, 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., .29802322387695312500e-7, .77471708843445529468e-6,
  .98649879372606876995e-5, .81814934772838523887e-4,
  .49554483992403011328e-3, .23290922072351413938e-2,
  .88068134250844034186e-2, .27393666952485719070e-1, 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., .14901161193847656250e-7, .40226235946098233685e-6,
  .53236418690561306700e-5, .45933829691164002269e-4,
  .28982005232838857913e-3, .14212974043211018374e-2,
  .56192363087488842264e-2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  .74505805969238281250e-8, .20858299254133430408e-6,
  .28648457300134381744e-5, .25677535898258910850e-4,
  .16849420429491355445e-3, .86062824010315834002e-3, 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., .37252902984619140625e-8, .10801736017613096861e-6,
  .15376606719887104015e-5, .14296523739727437959e-4,
  .97419023656050887203e-4, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  .18626451492309570312e-8, .55871592916438890146e-7,
  .82331193828137454068e-6, .79302250528382787666e-5, 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., .93132257461547851562e-9,
  .28867244235852488244e-7, .43982811713864556957e-6, 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., .46566128730773925781e-9,
  .14899342093408253335e-7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
  0., 0., .23283064365386962891e-9
};

/* Allocates a workspace for the given maximum number of intervals.
    Note that if the workspace gets filled, the intervals with the
    lowest error estimates are dropped. The maximum number of
    intervals is therefore not the maximum number of intervals
    that will be computed, but merely the size of the buffer.
    */

/* Compute the product of the fx with one of the inverse
    Vandermonde-like matrices. */

void
Vinvfx (const double *fx, double *c, const int d)
{

  int i, j;

  switch (d)
    {
    case 0:
      for (i = 0; i <= 4; i++)
        {
          c[i] = 0.0;
          for (j = 0; j <= 4; j++)
            c[i] += V1inv[i * 5 + j] * fx[j * 8];
        }
      break;
    case 1:
      for (i = 0; i <= 8; i++)
        {
          c[i] = 0.0;
          for (j = 0; j <= 8; j++)
            c[i] += V2inv[i * 9 + j] * fx[j * 4];
        }
      break;
    case 2:
      for (i = 0; i <= 16; i++)
        {
          c[i] = 0.0;
          for (j = 0; j <= 16; j++)
            c[i] += V3inv[i * 17 + j] * fx[j * 2];
        }
      break;
    case 3:
      for (i = 0; i <= 32; i++)
        {
          c[i] = 0.0;
          for (j = 0; j <= 32; j++)
            c[i] += V4inv[i * 33 + j] * fx[j];
        }
      break;
    }

}


/* Downdate the interpolation given by the n coefficients c
    by removing the nodes with indices in nans. */

void
downdate (double *c, int n, int d, int *nans, int nnans)
{

  static const int bidx[4] = { 0, 6, 16, 34 };
  double b_new[34], alpha;
  int i, j;

  for (i = 0; i <= n + 1; i++)
    b_new[i] = bee[bidx[d] + i];
  for (i = 0; i < nnans; i++)
    {
      b_new[n + 1] = b_new[n + 1] / Lalpha[n];
      b_new[n] = (b_new[n] + xi[nans[i]] * b_new[n + 1]) / Lalpha[n - 1];
      for (j = n - 1; j > 0; j--)
        b_new[j] =
          (b_new[j] + xi[nans[i]] * b_new[j + 1] -
           Lgamma[j + 1] * b_new[j + 2]) / Lalpha[j - 1];
      for (j = 0; j <= n; j++)
        b_new[j] = b_new[j + 1];
      alpha = c[n] / b_new[n];
      for (j = 0; j < n; j++)
        c[j] -= alpha * b_new[j];
      c[n] = 0;
      n--;
    }

}


/* The actual integration routine.  */

DEFUN (quadcc, args, nargout,
       "-*- texinfo -*-\n\
@deftypefn  {Function File} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b})\n\
@deftypefnx {Function File} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol})\n\
@deftypefnx {Function File} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})\n\
@deftypefnx {Function File} {[@var{q}, @var{err}, @var{nr_points}] =} quadcc (@dots{})\n\
Numerically evaluate the integral of @var{f} from @var{a} to @var{b}\n\
using the doubly-adaptive Clenshaw-Curtis quadrature described by P. Gonnet\n\
in @cite{Increasing the Reliability of Adaptive Quadrature Using Explicit\n\
Interpolants}.\n\
@var{f} is a function handle, inline function, or string\n\
containing the name of the function to evaluate.\n\
The function @var{f} must be vectorized and must return a vector of output\n\
values if given a vector of input values.  For example,\n\
\n\
@example\n\
f = @@(x) x .* sin (1./x) .* sqrt (abs (1 - x));\n\
@end example\n\
\n\
@noindent\n\
which uses the element-by-element ``dot'' form for all operators.\n\
\n\
@var{a} and @var{b} are the lower and upper limits of integration.  Either\n\
or both limits may be infinite.  @code{quadcc} handles an inifinite limit\n\
by substituting the variable of integration with @code{x = tan (pi/2*u)}.\n\
\n\
The optional argument @var{tol} defines the relative tolerance used to stop\n\
the integration procedure.  The default value is @math{1e^{-6}}.\n\
\n\
The optional argument @var{sing} contains a list of points where the\n\
integrand has known singularities, or discontinuities\n\
in any of its derivatives, inside the integration interval.\n\
For the example above, which has a discontinuity at x=1, the call to\n\
@code{quadcc} would be as follows\n\
\n\
@example\n\
int = quadcc (f, a, b, 1.0e-6, [ 1 ]);\n\
@end example\n\
\n\
The result of the integration is returned in @var{q}.\n\
@var{err} is an estimate of the absolute integration error and\n\
@var{nr_points} is the number of points at which the integrand was evaluated.\n\
If the adaptive integration did not converge, the value of\n\
@var{err} will be larger than the requested tolerance.  Therefore, it is\n\
recommended to verify this value for difficult integrands.\n\
\n\
@code{quadcc} is capable of dealing with non-numeric\n\
values of the integrand such as @code{NaN} or @code{Inf}.\n\
If the integral diverges, and @code{quadcc} detects this,\n\
then a warning is issued and @code{Inf} or @code{-Inf} is returned.\n\
\n\
Note: @code{quadcc} is a general purpose quadrature algorithm\n\
and, as such, may be less efficient for a smooth or otherwise\n\
well-behaved integrand than other methods such as @code{quadgk}.\n\
\n\
The algorithm uses Clenshaw-Curtis quadrature rules of increasing\n\
degree in each interval and bisects the interval if either the\n\
function does not appear to be smooth or a rule of maximum\n\
degree has been reached.  The error estimate is computed from the\n\
L2-norm of the difference between two successive interpolations\n\
of the integrand over the nodes of the respective quadrature rules.\n\
\n\
Reference: P. Gonnet, @cite{Increasing the Reliability of Adaptive\n\
Quadrature Using Explicit Interpolants}, ACM Transactions on\n\
Mathematical Software, Vol. 37, Issue 3, Article No. 3, 2010.\n\
@seealso{quad, quadv, quadl, quadgk, trapz, dblquad, triplequad}\n\
@end deftypefn")
{
  octave_value_list retval;

  /* Some constants that we will need. */
  static const int n[4] = { 4, 8, 16, 32 };
  static const int skip[4] = { 8, 4, 2, 1 };
  static const int idx[4] = { 0, 5, 14, 31 };
  static const double w = M_SQRT2 / 2;
  static const int ndiv_max = 20;

  /* Arguments left and right */
  int nargin = args.length ();
  octave_function *fcn;
  double a, b, tol, *sing;

  /* Variables needed for transforming the integrand. */
  bool wrap = false;
  double xw;

  /* Stuff we will need to call the integrand. */
  octave_value_list fargs, fvals;

  /* Actual variables (as opposed to constants above). */
  double m, h, ml, hl, mr, hr, temp;
  double igral, err, igral_final, err_final;
  int nivals, neval = 0;
  int i, j, d, split, t;
  int nnans, nans[33];
  cquad_ival *iv, *ivl, *ivr;
  double nc, ncdiff;


  /* Parse the input arguments. */
  if (nargin < 3)
    {
      print_usage ();
      return retval;
    }

  if (args(0).is_function_handle () || args(0).is_inline_function ())
    fcn = args(0).function_value ();
  else
    {
      std::string fcn_name = unique_symbol_name ("__quadcc_fcn__");
      std::string fname = "function y = ";
      fname.append (fcn_name);
      fname.append ("(x) y = ");
      fcn = extract_function (args(0), "quadcc", fcn_name, fname,
                              "; endfunction");
    }

  if (! args(1).is_real_scalar ())
    {
      error ("quadcc: lower limit of integration (A) must be a single real scalar");
      return retval;
    }
  else
    a = args(1).double_value ();

  if (! args(2).is_real_scalar ())
    {
      error ("quadcc: upper limit of integration (B) must be a single real scalar");
      return retval;
    }
  else
    b = args(2).double_value ();

  if (nargin < 4 || args(3).is_empty ())
    tol = 1.0e-6;
  else if (! args(3).is_real_scalar () || args(3).double_value () <= 0)
    {
      error ("quadcc: tolerance (TOL) must be a single real scalar > 0");
      return retval;
    }
  else
    tol = args(3).double_value ();

  if (nargin < 5)
    {
      nivals = 1;
    }
  else if (!(args(4).is_real_scalar () || args(4).is_real_matrix ()))
    {
      error ("quadcc: list of singularities (SING) must be a vector of real values");
      return retval;
    }
  else
    {
      nivals = 1 + args(4).numel ();
    }

  int cquad_heapsize = (nivals >= min_cquad_heapsize ? nivals + 1 
                                                     : min_cquad_heapsize);
  /* The interval heap. */
  OCTAVE_LOCAL_BUFFER (cquad_ival, ivals, cquad_heapsize);
  OCTAVE_LOCAL_BUFFER (double, iivals, cquad_heapsize);
  OCTAVE_LOCAL_BUFFER (int, heap, cquad_heapsize);

  if (nivals == 1)
    {
      iivals[0] = a;
      iivals[1] = b;
    }
  else
    {
      // Intervals around singularities
      sing = args(4).array_value ().fortran_vec ();
      iivals[0] = a;
      for (i = 0; i < nivals - 1; i++)
        iivals[i + 1] = sing[i];
      iivals[nivals] = b;
    }

  /* If a or b are +/-Inf, transform the integral. */
  if (xisinf (a) || xisinf (b))
    {
      wrap = true;
      for (i = 0; i < nivals + 1; i++)
        if (xisinf (iivals[i]))
          iivals[i] = gnulib::copysign (1.0, iivals[i]);
        else
          iivals[i] = 2.0 * atan (iivals[i]) / M_PI;
    }


  /* Initialize the heaps. */
  for (i = 0; i < cquad_heapsize; i++)
    heap[i] = i;

  /* Create the first interval(s). */
  igral = 0.0;
  err = 0.0;
  for (j = 0; j < nivals; j++)
    {

      /* Initialize the interval. */
      iv = &(ivals[heap[j]]);
      m = (iivals[j] + iivals[j + 1]) / 2;
      h = (iivals[j + 1] - iivals[j]) / 2;
      nnans = 0;
      ColumnVector ex (33);
      if (wrap)
        {
          for (i = 0; i <= n[3]; i++)
            ex(i) = tan (M_PI / 2 * (m + xi[i] * h));
        }
      else
        {
          for (i = 0; i <= n[3]; i++)
            ex(i) = m + xi[i] * h;
        }
      fargs(0) = ex;
      fvals = feval (fcn, fargs, 1);
      if (fvals.length () != 1 || ! fvals(0).is_real_matrix ())
        {
          error ("quadcc: integrand F must return a single, real-valued vector");
          return retval;
        }
      Matrix effex = fvals(0).matrix_value ();
      if (effex.length () != ex.length ())
        {
          error ("quadcc: integrand F must return a single, real-valued vector of the same size as the input");
          return retval;
        }
      for (i = 0; i <= n[3]; i++)
        {
          iv->fx[i] = effex(i);
          if (wrap)
            {
              xw = ex(i);
              iv->fx[i] *= (1.0 + xw * xw) * M_PI / 2;
            }
          neval++;
          if (! xfinite (iv->fx[i]))
            {
              nans[nnans++] = i;
              iv->fx[i] = 0.0;
            }
        }
      Vinvfx (iv->fx, &(iv->c[idx[3]]), 3);
      Vinvfx (iv->fx, &(iv->c[idx[2]]), 2);
      Vinvfx (iv->fx, &(iv->c[0]), 0);
      for (i = 0; i < nnans; i++)
        iv->fx[nans[i]] = octave_NaN;
      iv->a = iivals[j];
      iv->b = iivals[j + 1];
      iv->depth = 3;
      iv->rdepth = 1;
      iv->ndiv = 0;
      iv->igral = 2 * h * iv->c[idx[3]] * w;
      nc = 0.0;
      for (i = n[2] + 1; i <= n[3]; i++)
        {
          temp = iv->c[idx[3] + i];
          nc += temp * temp;
        }
      ncdiff = nc;
      for (i = 0; i <= n[2]; i++)
        {
          temp = iv->c[idx[2] + i] - iv->c[idx[3] + i];
          ncdiff += temp * temp;
          nc += iv->c[idx[3] + i] * iv->c[idx[3] + i];
        }
      ncdiff = sqrt (ncdiff);
      nc = sqrt (nc);
      iv->err = ncdiff * 2 * h;
      if (ncdiff / nc > 0.1 && iv->err < 2 * h * nc)
        iv->err = 2 * h * nc;

      /* Tabulate this interval's data. */
      igral += iv->igral;
      err += iv->err;

      /* Sift it up the heap. */
      i = j;
      while (i > 0 && ivals[heap[i / 2]].err < ivals[heap[i]].err)
        {
          temp = heap[i];
          heap[i] = heap[i / 2];
          heap[i / 2] = temp;
          i /= 2;
        }

    }


  /* Initialize some global values. */
  igral_final = 0.0;
  err_final = 0.0;


  /* Main loop. */
  while (nivals > 0 && err > 0.0 && err > fabs (igral) * tol
         && !(err_final > fabs (igral) * tol
              && err - err_final < fabs (igral) * tol))
    {

      /* Allow the user to interrupt. */
      OCTAVE_QUIT;

      /* Put our finger on the interval with the largest error. */
      iv = &(ivals[heap[0]]);
      m = (iv->a + iv->b) / 2;
      h = (iv->b - iv->a) / 2;

#if (DEBUG_QUADCC)
      printf ("quadcc: processing ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
              heap[0], nivals, iv->a, iv->b, iv->igral, iv->err, iv->depth);
#endif

      /* Should we try to increase the degree? */
      if (iv->depth < 3)
        {

          /* Keep tabs on some variables. */
          d = ++iv->depth;

          /* Get the new (missing) function values */
          {
            ColumnVector ex (n[d] / 2);
            if (wrap)
              {
                for (i = 0; i < n[d] / 2; i++)
                  ex(i) = tan (M_PI / 2 * (m + xi[(2 * i + 1) * skip[d]] * h));
              }
            else
              {
                for (i = 0; i < n[d] / 2; i++)
                  ex(i) = m + xi[(2 * i + 1) * skip[d]] * h;
              }
            fargs(0) = ex;
            fvals = feval (fcn, fargs, 1);
            if (fvals.length () != 1 || ! fvals(0).is_real_matrix ())
              {
                error ("quadcc: integrand F must return a single, real-valued vector");
                return retval;
              }
            Matrix effex = fvals(0).matrix_value ();
            if (effex.length () != ex.length ())
              {
                error ("quadcc: integrand F must return a single, real-valued vector of the same size as the input");
                return retval;
              }
            neval += effex.length ();
            for (i = 0; i < n[d] / 2; i++)
              {
                j = (2 * i + 1) * skip[d];
                iv->fx[j] = effex(i);
                if (wrap)
                  {
                    xw = ex(i);
                    iv->fx[j] *= (1.0 + xw * xw) * M_PI / 2;
                  }
              }
          }
          nnans = 0;
          for (i = 0; i <= 32; i += skip[d])
            {
              if (! xfinite (iv->fx[i]))
                {
                  nans[nnans++] = i;
                  iv->fx[i] = 0.0;
                }
            }

          /* Compute the new coefficients. */
          Vinvfx (iv->fx, &(iv->c[idx[d]]), d);
          /* Downdate any NaNs. */
          if (nnans > 0)
            {
              downdate (&(iv->c[idx[d]]), n[d], d, nans, nnans);
              for (i = 0; i < nnans; i++)
                iv->fx[nans[i]] = octave_NaN;
            }

          /* Compute the error estimate. */
          nc = 0.0;
          for (i = n[d - 1] + 1; i <= n[d]; i++)
            {
              temp = iv->c[idx[d] + i];
              nc += temp * temp;
            }
          ncdiff = nc;
          for (i = 0; i <= n[d - 1]; i++)
            {
              temp = iv->c[idx[d - 1] + i] - iv->c[idx[d] + i];
              ncdiff += temp * temp;
              nc += iv->c[idx[d] + i] * iv->c[idx[d] + i];
            }
          ncdiff = sqrt (ncdiff);
          nc = sqrt (nc);
          iv->err = ncdiff * 2 * h;
          /* Compute the local integral. */
          iv->igral = 2 * h * w * iv->c[idx[d]];
          /* Split the interval prematurely? */
          split = (nc > 0 && ncdiff / nc > 0.1);
        }

      /* Maximum degree reached, just split. */
      else
        {
          split = 1;
        }


      /* Should we drop this interval? */
      if ((m + h * xi[0]) >= (m + h * xi[1])
          || (m + h * xi[31]) >= (m + h * xi[32])
          || iv->err < fabs (iv->igral)
                       * std::numeric_limits<double>::epsilon () * 10)
        {

#if (DEBUG_QUADCC)
          printf ("quadcc: dropping ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
                  heap[0], nivals, iv->a, iv->b, iv->igral, iv->err, iv->depth);
#endif

          /* Keep this interval's contribution */
          err_final += iv->err;
          igral_final += iv->igral;
          /* Swap with the last element on the heap */
          t = heap[nivals - 1];
          heap[nivals - 1] = heap[0];
          heap[0] = t;
          nivals--;
          /* Fix up the heap */
          i = 0;
          while (2 * i + 1 < nivals)
            {
              /* Get the kids */
              j = 2 * i + 1;
              /* If the j+1st entry exists and is larger than the jth,
                 use it instead. */
              if (j + 1 < nivals
                  && ivals[heap[j + 1]].err >= ivals[heap[j]].err)
                j++;
              /* Do we need to move the ith entry up? */
              if (ivals[heap[j]].err <= ivals[heap[i]].err)
                break;
              else
                {
                  t = heap[j];
                  heap[j] = heap[i];
                  heap[i] = t;
                  i = j;
                }
            }

        }

      /* Do we need to split this interval? */
      else if (split)
        {

          /* Some values we will need often... */
          d = iv->depth;
          /* Generate the interval on the left */
          ivl = &(ivals[heap[nivals++]]);
          ivl->a = iv->a;
          ivl->b = m;
          ml = (ivl->a + ivl->b) / 2;
          hl = h / 2;
          ivl->depth = 0;
          ivl->rdepth = iv->rdepth + 1;
          ivl->fx[0] = iv->fx[0];
          ivl->fx[32] = iv->fx[16];
          {
            ColumnVector ex (n[0] - 1);
            if (wrap)
              {
                for (i = 0; i < n[0] - 1; i++)
                  ex(i) = tan (M_PI / 2 * (ml + xi[(i + 1) * skip[0]] * hl));
              }
            else
              {
                for (i = 0; i < n[0] - 1; i++)
                  ex(i) = ml + xi[(i + 1) * skip[0]] * hl;
              }
            fargs(0) = ex;
            fvals = feval (fcn, fargs, 1);
            if (fvals.length () != 1 || ! fvals(0).is_real_matrix ())
              {
                error ("quadcc: integrand F must return a single, real-valued vector");
                return retval;
              }
            Matrix effex = fvals(0).matrix_value ();
            if (effex.length () != ex.length ())
              {
                error ("quadcc: integrand F must return a single, real-valued vector of the same size as the input");
                return retval;
              }
            neval += effex.length ();
            for (i = 0; i < n[0] - 1; i++)
              {
                j = (i + 1) * skip[0];
                ivl->fx[j] = effex(i);
                if (wrap)
                  {
                    xw = ex(i);
                    ivl->fx[j] *= (1.0 + xw * xw) * M_PI / 2;
                  }
              }
          }
          nnans = 0;
          for (i = 0; i <= 32; i += skip[0])
            {
              if (! xfinite (ivl->fx[i]))
                {
                  nans[nnans++] = i;
                  ivl->fx[i] = 0.0;
                }
            }
          Vinvfx (ivl->fx, ivl->c, 0);
          if (nnans > 0)
            {
              downdate (ivl->c, n[0], 0, nans, nnans);
              for (i = 0; i < nnans; i++)
                ivl->fx[nans[i]] = octave_NaN;
            }
          for (i = 0; i <= n[d]; i++)
            {
              ivl->c[idx[d] + i] = 0.0;
              for (j = i; j <= n[d]; j++)
                ivl->c[idx[d] + i] += Tleft[i * 33 + j] * iv->c[idx[d] + j];
            }
          ncdiff = 0.0;
          for (i = 0; i <= n[0]; i++)
            {
              temp = ivl->c[i] - ivl->c[idx[d] + i];
              ncdiff += temp * temp;
            }
          for (i = n[0] + 1; i <= n[d]; i++)
            {
              temp = ivl->c[idx[d] + i];
              ncdiff += temp * temp;
            }
          ncdiff = sqrt (ncdiff);
          ivl->err = ncdiff * h;
          /* Check for divergence. */
          ivl->ndiv = iv->ndiv + (fabs (iv->c[0]) > 0
                                  && ivl->c[0] / iv->c[0] > 2);
          if (ivl->ndiv > ndiv_max && 2 * ivl->ndiv > ivl->rdepth)
            {
              igral = gnulib::copysign (octave_Inf, igral);
              warning ("quadcc: divergent integral detected");
              break;
            }

          /* Compute the local integral. */
          ivl->igral = h * w * ivl->c[0];


          /* Generate the interval on the right */
          ivr = &(ivals[heap[nivals++]]);
          ivr->a = m;
          ivr->b = iv->b;
          mr = (ivr->a + ivr->b) / 2;
          hr = h / 2;
          ivr->depth = 0;
          ivr->rdepth = iv->rdepth + 1;
          ivr->fx[0] = iv->fx[16];
          ivr->fx[32] = iv->fx[32];
          {
            ColumnVector ex (n[0] - 1);
            if (wrap)
              {
                for (i = 0; i < n[0] - 1; i++)
                  ex(i) = tan (M_PI / 2 * (mr + xi[(i + 1) * skip[0]] * hr));
              }
            else
              {
                for (i = 0; i < n[0] - 1; i++)
                  ex(i) = mr + xi[(i + 1) * skip[0]] * hr;
              }
            fargs(0) = ex;
            fvals = feval (fcn, fargs, 1);
            if (fvals.length () != 1 || ! fvals(0).is_real_matrix ())
              {
                error ("quadcc: integrand F must return a single, real-valued vector");
                return retval;
              }
            Matrix effex = fvals(0).matrix_value ();
            if (effex.length () != ex.length ())
              {
                error ("quadcc: integrand F must return a single, real-valued vector of the same size as the input");
                return retval;
              }
            neval += effex.length ();
            for (i = 0; i < n[0] - 1; i++)
              {
                j = (i + 1) * skip[0];
                ivr->fx[j] = effex(i);
                if (wrap)
                  {
                    xw = ex(i);
                    ivr->fx[j] *= (1.0 + xw * xw) * M_PI / 2;
                  }
              }
          }
          nnans = 0;
          for (i = 0; i <= 32; i += skip[0])
            {
              if (! xfinite (ivr->fx[i]))
                {
                  nans[nnans++] = i;
                  ivr->fx[i] = 0.0;
                }
            }
          Vinvfx (ivr->fx, ivr->c, 0);
          if (nnans > 0)
            {
              downdate (ivr->c, n[0], 0, nans, nnans);
              for (i = 0; i < nnans; i++)
                ivr->fx[nans[i]] = octave_NaN;
            }
          for (i = 0; i <= n[d]; i++)
            {
              ivr->c[idx[d] + i] = 0.0;
              for (j = i; j <= n[d]; j++)
                ivr->c[idx[d] + i] += Tright[i * 33 + j] * iv->c[idx[d] + j];
            }
          ncdiff = 0.0;
          for (i = 0; i <= n[0]; i++)
            {
              temp = ivr->c[i] - ivr->c[idx[d] + i];
              ncdiff += temp * temp;
            }
          for (i = n[0] + 1; i <= n[d]; i++)
            {
              temp = ivr->c[idx[d] + i];
              ncdiff += temp * temp;
            }
          ncdiff = sqrt (ncdiff);
          ivr->err = ncdiff * h;
          /* Check for divergence. */
          ivr->ndiv = iv->ndiv + (fabs (iv->c[0]) > 0
                                  && ivr->c[0] / iv->c[0] > 2);
          if (ivr->ndiv > ndiv_max && 2 * ivr->ndiv > ivr->rdepth)
            {
              igral = gnulib::copysign (octave_Inf, igral);
              warning ("quadcc: divergent integral detected");
              break;
            }

          /* Compute the local integral. */
          ivr->igral = h * w * ivr->c[0];


          /* Fix-up the heap: we now have one interval on top
             that we don't need any more and two new, unsorted
             ones at the bottom. */
          /* Flip the last interval to the top of the heap and
             sift down. */
          t = heap[nivals - 1];
          heap[nivals - 1] = heap[0];
          heap[0] = t;
          nivals--;
          /* Sift this interval back down the heap. */
          i = 0;
          while (2 * i + 1 < nivals - 1)
            {
              j = 2 * i + 1;
              if (j + 1 < nivals - 1
                  && ivals[heap[j + 1]].err >= ivals[heap[j]].err)
                j++;
              if (ivals[heap[j]].err <= ivals[heap[i]].err)
                break;
              else
                {
                  t = heap[j];
                  heap[j] = heap[i];
                  heap[i] = t;
                  i = j;
                }
            }

          /* Now grab the last interval and sift it up the heap. */
          i = nivals - 1;
          while (i > 0)
            {
              j = (i - 1) / 2;
              if (ivals[heap[j]].err < ivals[heap[i]].err)
                {
                  t = heap[j];
                  heap[j] = heap[i];
                  heap[i] = t;
                  i = j;
                }
              else
                break;
            }


        }

      /* Otherwise, just fix-up the heap. */
      else
        {
          i = 0;
          while (2 * i + 1 < nivals)
            {
              j = 2 * i + 1;
              if (j + 1 < nivals
                  && ivals[heap[j + 1]].err >= ivals[heap[j]].err)
                j++;
              if (ivals[heap[j]].err <= ivals[heap[i]].err)
                break;
              else
                {
                  t = heap[j];
                  heap[j] = heap[i];
                  heap[i] = t;
                  i = j;
                }
            }

        }

      /* If the heap is about to overflow, remove the last two intervals. */
      while (nivals > cquad_heapsize - 2)
        {
          iv = &(ivals[heap[nivals - 1]]);
#if (DEBUG_QUADCC)
          printf ("quadcc: dropping ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
                  heap[0], nivals, iv->a, iv->b, iv->igral, iv->err, iv->depth);
#endif
          err_final += iv->err;
          igral_final += iv->igral;
          nivals--;
        }

      /* Collect the value of the integral and error. */
      igral = igral_final;
      err = err_final;
      for (i = 0; i < nivals; i++)
        {
          igral += ivals[heap[i]].igral;
          err += ivals[heap[i]].err;
        }

    }

  /* Dump the contents of the heap. */
#if (DEBUG_QUADCC)
  for (i = 0; i < nivals; i++)
    {
      iv = &(ivals[heap[i]]);
      printf ("quadcc: ival %i (%i) with [%e,%e], int=%e, err=%e, depth=%i, rdepth=%i, ndiv=%i\n",
              i, heap[i], iv->a, iv->b, iv->igral, iv->err, iv->depth,
              iv->rdepth, iv->ndiv);
    }
#endif

  /* Clean up and present the results. */
  if (nargout > 2)
    retval(2) = neval;
  if (nargout > 1)
    retval(1) = err;
  retval(0) = igral;
  /* All is well that ends well. */
  return retval;
}


/*
%!assert (quadcc (@sin, -pi, pi), 0, 1e-6)
%!assert (quadcc (inline ("sin"),- pi, pi), 0, 1e-6)
%!assert (quadcc ("sin", -pi, pi), 0, 1e-6)

%!assert (quadcc (@sin, -pi, 0), -2, 1e-6)
%!assert (quadcc (@sin, 0, pi), 2, 1e-6)
%!assert (quadcc (@(x) 1./sqrt (x), 0, 1), 2, 1e-6)
%!assert (quadcc (@(x) 1./(sqrt (x).*(x+1)), 0, Inf), pi, 1e-6)

%!assert (quadcc (@(x) exp (-x .^ 2), -Inf, Inf), sqrt (pi), 1e-6)
%!assert (quadcc (@(x) exp (-x .^ 2), -Inf, 0), sqrt (pi)/2, 1e-6)

## Test function with NaNs in interval
%!function y = __nansin (x)
%!  nan_locs = [-3*pi/4, -pi/4, 0, pi/3, pi/2, pi];
%!  y = sin (x);
%!  idx = min (abs (bsxfun (@minus, x(:), nan_locs)), [], 2);
%!  y(idx < 1e-10) = NaN;
%!endfunction

%!test
%! [q, err, npoints] = quadcc ("__nansin", -pi, pi);
%! assert (q, 0, 1e-6);
%! assert (err, 0, 15*eps);

%% Test input validation
%!error (quadcc ())
%!error (quadcc (@sin))
%!error (quadcc (@sin, 0))
%!error (quadcc (@sin, ones (2), pi))
%!error (quadcc (@sin, -i, pi))
%!error (quadcc (@sin, 0, ones (2)))
%!error (quadcc (@sin, 0, i))
%!error (quadcc (@sin, 0, pi, 0))
%!error (quadcc (@sin, 0, pi, 1e-6, [ i ]))
*/