IntegrationRules.cpp

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/**
 * \file IntegrationRules.cpp
 *
 * Integration rules
 *
 */
 
 
 
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <time.h>
#include <IntegrationRules.hpp>
 
namespace MoFEM {
 
namespace IntRules {
 
namespace NCC {
 
#include <triangle_ncc_rule.c>
#include <tetrahedron_ncc_rule.c>
 
} // namespace NCC
 
namespace NCO {
 
#include <triangle_nco_rule.c>
#include <tetrahedron_nco_rule.c>
 
} // namespace NCO
 
/**
 * Xiao--Gimbutas rules Q000002, downloaded from:
 * https://quadraturerules.org/Q000002
 *
 * Copyright quadraturerules.org contributors, reused under CC BY 4.0.
 * The original Xiao--Gimbutas publication is:
 * https://doi.org/10.1016/j.camwa.2009.10.027
 */
namespace XiaoGimbutas {
namespace {
const double triangleRule1Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
};
const double triangleRule1Weights[] = {
  1.0,
};
const double triangleRule2Points[] = {
  0.6666666666666667, 0.16666666666666666, 0.16666666666666666,
  0.16666666666666663, 0.16666666666666666, 0.6666666666666667,
  0.16666666666666663, 0.6666666666666667, 0.16666666666666666,
};
const double triangleRule2Weights[] = {
  0.3333333333333333,
  0.3333333333333333,
  0.3333333333333333,
};
const double triangleRule3Points[] = {
  0.10810301816807022, 0.4459484909159649, 0.4459484909159649,
  0.8168475729804583, 0.09157621350977085, 0.09157621350977085,
  0.4459484909159649, 0.4459484909159649, 0.10810301816807022,
  0.09157621350977085, 0.09157621350977085, 0.8168475729804583,
  0.4459484909159649, 0.10810301816807022, 0.4459484909159649,
  0.09157621350977085, 0.8168475729804583, 0.09157621350977085,
};
const double triangleRule3Weights[] = {
  0.22338158967801147,
  0.10995174365532188,
  0.22338158967801147,
  0.10995174365532188,
  0.22338158967801147,
  0.10995174365532188,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double triangleRule4Points[] = {
  0.10810301816807022, 0.4459484909159649, 0.4459484909159649,
  0.8168475729804583, 0.09157621350977085, 0.09157621350977085,
  0.4459484909159649, 0.4459484909159649, 0.10810301816807022,
  0.09157621350977085, 0.09157621350977085, 0.8168475729804583,
  0.4459484909159649, 0.10810301816807022, 0.4459484909159649,
  0.09157621350977085, 0.8168475729804583, 0.09157621350977085,
};
const double triangleRule4Weights[] = {
  0.22338158967801147,
  0.10995174365532188,
  0.22338158967801147,
  0.10995174365532188,
  0.22338158967801147,
  0.10995174365532188,
};
const double triangleRule5Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.7974269853530872, 0.1012865073234564, 0.1012865073234564,
  0.05971587178976989, 0.47014206410511505, 0.47014206410511505,
  0.10128650732345634, 0.1012865073234564, 0.7974269853530872,
  0.47014206410511505, 0.47014206410511505, 0.05971587178976989,
  0.10128650732345634, 0.7974269853530872, 0.1012865073234564,
  0.47014206410511505, 0.05971587178976989, 0.47014206410511505,
};
const double triangleRule5Weights[] = {
  0.225,
  0.12593918054482714,
  0.1323941527885062,
  0.12593918054482714,
  0.1323941527885062,
  0.12593918054482714,
  0.1323941527885062,
};
const double triangleRule6Points[] = {
  0.561140034900434, 0.21942998254978302, 0.21942998254978302,
  0.039724071775569914, 0.48013796411221504, 0.48013796411221504,
  0.21942998254978296, 0.21942998254978302, 0.561140034900434,
  0.480137964112215, 0.48013796411221504, 0.039724071775569914,
  0.21942998254978296, 0.561140034900434, 0.21942998254978302,
  0.480137964112215, 0.039724071775569914, 0.48013796411221504,
  0.8390092597147911, 0.019371724361240805, 0.14161901592396814,
  0.14161901592396808, 0.8390092597147911, 0.019371724361240805,
  0.019371724361240794, 0.14161901592396814, 0.8390092597147911,
  0.8390092597147911, 0.14161901592396814, 0.019371724361240805,
  0.019371724361240794, 0.8390092597147911, 0.14161901592396814,
  0.14161901592396808, 0.019371724361240805, 0.8390092597147911,
};
const double triangleRule6Weights[] = {
  0.17133312415298105,
  0.08073108959303098,
  0.17133312415298105,
  0.08073108959303098,
  0.17133312415298105,
  0.08073108959303098,
  0.04063455979366066,
  0.04063455979366066,
  0.04063455979366066,
  0.04063455979366066,
  0.04063455979366066,
  0.04063455979366066,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double triangleRule7Points[] = {
  0.05360869262149792, 0.47319565368925104, 0.47319565368925104,
  0.884404719890987, 0.057797640054506494, 0.057797640054506494,
  0.5166727872055051, 0.24166360639724743, 0.24166360639724743,
  0.473195653689251, 0.47319565368925104, 0.05360869262149792,
  0.057797640054506494, 0.057797640054506494, 0.884404719890987,
  0.2416636063972475, 0.24166360639724743, 0.5166727872055051,
  0.473195653689251, 0.05360869262149792, 0.47319565368925104,
  0.057797640054506494, 0.884404719890987, 0.057797640054506494,
  0.2416636063972475, 0.5166727872055051, 0.24166360639724743,
  0.6936897820041288, 0.046971206130085534, 0.2593390118657857,
  0.2593390118657857, 0.6936897820041288, 0.046971206130085534,
  0.04697120613008554, 0.2593390118657857, 0.6936897820041288,
  0.6936897820041288, 0.2593390118657857, 0.046971206130085534,
  0.04697120613008554, 0.6936897820041288, 0.2593390118657857,
  0.2593390118657857, 0.046971206130085534, 0.6936897820041288,
};
const double triangleRule7Weights[] = {
  0.05318083329676046,
  0.04091817039405687,
  0.12772524856113385,
  0.05318083329676046,
  0.04091817039405687,
  0.12772524856113385,
  0.05318083329676046,
  0.04091817039405687,
  0.12772524856113385,
  0.055754540540691094,
  0.055754540540691094,
  0.055754540540691094,
  0.055754540540691094,
  0.055754540540691094,
  0.055754540540691094,
};
const double triangleRule8Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.6588613844964795, 0.17056930775176027, 0.17056930775176027,
  0.08141482341455375, 0.4592925882927231, 0.4592925882927231,
  0.8989055433659379, 0.05054722831703107, 0.05054722831703107,
  0.17056930775176027, 0.17056930775176027, 0.6588613844964795,
  0.4592925882927231, 0.4592925882927231, 0.08141482341455375,
  0.05054722831703107, 0.05054722831703107, 0.8989055433659379,
  0.17056930775176027, 0.6588613844964795, 0.17056930775176027,
  0.4592925882927231, 0.08141482341455375, 0.4592925882927231,
  0.05054722831703107, 0.8989055433659379, 0.05054722831703107,
  0.7284923929554042, 0.008394777409957675, 0.26311282963463806,
  0.263112829634638, 0.7284923929554044, 0.008394777409957675,
  0.008394777409957532, 0.26311282963463806, 0.7284923929554044,
  0.7284923929554042, 0.26311282963463806, 0.008394777409957675,
  0.008394777409957532, 0.7284923929554044, 0.26311282963463806,
  0.263112829634638, 0.008394777409957675, 0.7284923929554044,
};
const double triangleRule8Weights[] = {
  0.1443156076777872,
  0.10321737053471824,
  0.09509163426728463,
  0.03245849762319808,
  0.10321737053471824,
  0.09509163426728463,
  0.03245849762319808,
  0.10321737053471824,
  0.09509163426728463,
  0.03245849762319808,
  0.027230314174434996,
  0.027230314174434996,
  0.027230314174434996,
  0.027230314174434996,
  0.027230314174434996,
  0.027230314174434996,
};
const double triangleRule9Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.02063496160252476, 0.4896825191987376, 0.4896825191987376,
  0.6235929287619344, 0.1882035356190328, 0.1882035356190328,
  0.12582081701412673, 0.43708959149293664, 0.43708959149293664,
  0.9105409732110945, 0.04472951339445275, 0.04472951339445275,
  0.4896825191987376, 0.4896825191987376, 0.02063496160252476,
  0.1882035356190328, 0.1882035356190328, 0.6235929287619344,
  0.4370895914929367, 0.43708959149293664, 0.12582081701412673,
  0.04472951339445275, 0.04472951339445275, 0.9105409732110945,
  0.4896825191987376, 0.02063496160252476, 0.4896825191987376,
  0.1882035356190328, 0.6235929287619344, 0.1882035356190328,
  0.4370895914929367, 0.12582081701412673, 0.43708959149293664,
  0.04472951339445275, 0.9105409732110945, 0.04472951339445275,
  0.741198598784498, 0.0368384120547363, 0.2219629891607657,
  0.22196298916076573, 0.741198598784498, 0.0368384120547363,
  0.03683841205473626, 0.2219629891607657, 0.741198598784498,
  0.741198598784498, 0.2219629891607657, 0.0368384120547363,
  0.03683841205473626, 0.741198598784498, 0.2219629891607657,
  0.22196298916076573, 0.0368384120547363, 0.741198598784498,
};
const double triangleRule9Weights[] = {
  0.09713579628279884,
  0.03133470022713907,
  0.07964773892721026,
  0.07782754100477428,
  0.025577675658698035,
  0.03133470022713907,
  0.07964773892721026,
  0.07782754100477428,
  0.025577675658698035,
  0.03133470022713907,
  0.07964773892721026,
  0.07782754100477428,
  0.025577675658698035,
  0.043283539377289376,
  0.043283539377289376,
  0.043283539377289376,
  0.043283539377289376,
  0.043283539377289376,
  0.043283539377289376,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double triangleRule10Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.009653080397658997, 0.4951734598011705, 0.4951734598011705,
  0.9617211695143174, 0.019139415242841296, 0.019139415242841296,
  0.6310299746295069, 0.18448501268524653, 0.18448501268524653,
  0.14353035811256232, 0.42823482094371884, 0.42823482094371884,
  0.49517345980117056, 0.4951734598011705, 0.009653080397658997,
  0.01913941524284124, 0.019139415242841296, 0.9617211695143174,
  0.18448501268524653, 0.18448501268524653, 0.6310299746295069,
  0.4282348209437188, 0.42823482094371884, 0.14353035811256232,
  0.49517345980117056, 0.009653080397658997, 0.4951734598011705,
  0.01913941524284124, 0.9617211695143174, 0.019139415242841296,
  0.18448501268524653, 0.6310299746295069, 0.18448501268524653,
  0.4282348209437188, 0.14353035811256232, 0.42823482094371884,
  0.8315416244168035, 0.03472362048232748, 0.13373475510086913,
  0.6357241363774715, 0.03758272734119169, 0.3266931362813369,
  0.13373475510086907, 0.8315416244168035, 0.03472362048232748,
  0.3266931362813369, 0.6357241363774714, 0.03758272734119169,
  0.034723620482327355, 0.13373475510086913, 0.8315416244168035,
  0.037582727341191724, 0.3266931362813369, 0.6357241363774714,
  0.8315416244168035, 0.13373475510086913, 0.03472362048232748,
  0.6357241363774715, 0.3266931362813369, 0.03758272734119169,
  0.034723620482327355, 0.8315416244168035, 0.13373475510086913,
  0.037582727341191724, 0.6357241363774714, 0.3266931362813369,
  0.13373475510086907, 0.03472362048232748, 0.8315416244168035,
  0.3266931362813369, 0.03758272734119169, 0.6357241363774714,
};
const double triangleRule10Weights[] = {
  0.08361487437397393,
  0.009792590498418303,
  0.006385359230118654,
  0.07863376974637727,
  0.07524732796854398,
  0.009792590498418303,
  0.006385359230118654,
  0.07863376974637727,
  0.07524732796854398,
  0.009792590498418303,
  0.006385359230118654,
  0.07863376974637727,
  0.07524732796854398,
  0.028962281463256342,
  0.038739049086018905,
  0.028962281463256342,
  0.038739049086018905,
  0.028962281463256342,
  0.038739049086018905,
  0.028962281463256342,
  0.038739049086018905,
  0.028962281463256342,
  0.038739049086018905,
  0.028962281463256342,
  0.038739049086018905,
};
const double triangleRule11Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.9383062087288238, 0.030846895635588123, 0.030846895635588123,
  0.0024396696430785125, 0.49878016517846074, 0.49878016517846074,
  0.7735843454266119, 0.11320782728669404, 0.11320782728669404,
  0.12668996721364778, 0.4366550163931761, 0.4366550163931761,
  0.5710330827614613, 0.21448345861926937, 0.21448345861926937,
  0.030846895635588067, 0.030846895635588123, 0.9383062087288238,
  0.4987801651784607, 0.49878016517846074, 0.0024396696430785125,
  0.1132078272866941, 0.11320782728669404, 0.7735843454266119,
  0.43665501639317617, 0.4366550163931761, 0.12668996721364778,
  0.21448345861926943, 0.21448345861926937, 0.5710330827614613,
  0.030846895635588067, 0.9383062087288238, 0.030846895635588123,
  0.4987801651784607, 0.0024396696430785125, 0.49878016517846074,
  0.1132078272866941, 0.7735843454266119, 0.11320782728669404,
  0.43665501639317617, 0.12668996721364778, 0.4366550163931761,
  0.21448345861926943, 0.5710330827614613, 0.21448345861926937,
  0.8263297175927509, 0.014366662569555624, 0.1593036198376935,
  0.6417047167143861, 0.04766406697215078, 0.31063121631346313,
  0.15930361983769348, 0.8263297175927509, 0.014366662569555624,
  0.31063121631346313, 0.6417047167143861, 0.04766406697215078,
  0.014366662569555655, 0.1593036198376935, 0.8263297175927509,
  0.047664066972150754, 0.31063121631346313, 0.6417047167143861,
  0.8263297175927509, 0.1593036198376935, 0.014366662569555624,
  0.6417047167143861, 0.31063121631346313, 0.04766406697215078,
  0.014366662569555655, 0.8263297175927509, 0.1593036198376935,
  0.047664066972150754, 0.6417047167143861, 0.31063121631346313,
  0.15930361983769348, 0.014366662569555624, 0.8263297175927509,
  0.31063121631346313, 0.04766406697215078, 0.6417047167143861,
};
const double triangleRule11Weights[] = {
  0.08144513470935129,
  0.012249296950707964,
  0.012465491873881381,
  0.04012924238130832,
  0.06309487215989869,
  0.06784510774369515,
  0.012249296950707964,
  0.012465491873881381,
  0.04012924238130832,
  0.06309487215989869,
  0.06784510774369515,
  0.012249296950707964,
  0.012465491873881381,
  0.04012924238130832,
  0.06309487215989869,
  0.06784510774369515,
  0.014557623337809246,
  0.04064284865588647,
  0.014557623337809246,
  0.04064284865588647,
  0.014557623337809246,
  0.04064284865588647,
  0.014557623337809246,
  0.04064284865588647,
  0.014557623337809246,
  0.04064284865588647,
  0.014557623337809246,
  0.04064284865588647,
};
const double triangleRule12Points[] = {
  0.45707498597014773, 0.27146250701492614, 0.27146250701492614,
  0.7814843446812914, 0.10925782765935432, 0.10925782765935432,
  0.11977670268281382, 0.4401116486585931, 0.4401116486585931,
  0.02359249810891695, 0.4882037509455415, 0.4882037509455415,
  0.9507072731273287, 0.02464636343633564, 0.02464636343633564,
  0.27146250701492614, 0.27146250701492614, 0.45707498597014773,
  0.10925782765935432, 0.10925782765935432, 0.7814843446812914,
  0.4401116486585931, 0.4401116486585931, 0.11977670268281382,
  0.48820375094554147, 0.4882037509455415, 0.02359249810891695,
  0.02464636343633564, 0.02464636343633564, 0.9507072731273287,
  0.27146250701492614, 0.45707498597014773, 0.27146250701492614,
  0.10925782765935432, 0.7814843446812914, 0.10925782765935432,
  0.4401116486585931, 0.11977670268281382, 0.4401116486585931,
  0.48820375094554147, 0.02359249810891695, 0.4882037509455415,
  0.02464636343633564, 0.9507072731273287, 0.02464636343633564,
  0.628249751683556, 0.1162960196779266, 0.25545422863851736,
  0.85133779251024, 0.021382490256170623, 0.12727971723358936,
  0.6853101639063919, 0.023034156355267166, 0.29165567973834094,
  0.2554542286385173, 0.6282497516835561, 0.1162960196779266,
  0.12727971723358933, 0.85133779251024, 0.021382490256170623,
  0.29165567973834094, 0.6853101639063919, 0.023034156355267166,
  0.11629601967792658, 0.25545422863851736, 0.6282497516835561,
  0.021382490256170672, 0.12727971723358936, 0.85133779251024,
  0.023034156355267177, 0.29165567973834094, 0.6853101639063919,
  0.628249751683556, 0.25545422863851736, 0.1162960196779266,
  0.85133779251024, 0.12727971723358936, 0.021382490256170623,
  0.6853101639063919, 0.29165567973834094, 0.023034156355267166,
  0.11629601967792658, 0.6282497516835561, 0.25545422863851736,
  0.021382490256170672, 0.85133779251024, 0.12727971723358936,
  0.023034156355267177, 0.6853101639063919, 0.29165567973834094,
  0.2554542286385173, 0.1162960196779266, 0.6282497516835561,
  0.12727971723358933, 0.021382490256170623, 0.85133779251024,
  0.29165567973834094, 0.023034156355267166, 0.6853101639063919,
};
const double triangleRule12Weights[] = {
  0.06254121319590276,
  0.02848605206887755,
  0.04991833492806095,
  0.024266838081452035,
  0.007931642509973639,
  0.06254121319590276,
  0.02848605206887755,
  0.04991833492806095,
  0.024266838081452035,
  0.007931642509973639,
  0.06254121319590276,
  0.02848605206887755,
  0.04991833492806095,
  0.024266838081452035,
  0.007931642509973639,
  0.04322736365941421,
  0.015083677576511441,
  0.02178358503860756,
  0.04322736365941421,
  0.015083677576511441,
  0.02178358503860756,
  0.04322736365941421,
  0.015083677576511441,
  0.02178358503860756,
  0.04322736365941421,
  0.015083677576511441,
  0.02178358503860756,
  0.04322736365941421,
  0.015083677576511441,
  0.02178358503860756,
  0.04322736365941421,
  0.015083677576511441,
  0.02178358503860756,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double triangleRule13Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.007728210517907841, 0.4961358947410461, 0.4961358947410461,
  0.06078262069301621, 0.4696086896534919, 0.4696086896534919,
  0.5377794301018355, 0.23111028494908226, 0.23111028494908226,
  0.17104485944189085, 0.4144775702790546, 0.4144775702790546,
  0.7728801748557335, 0.11355991257213327, 0.11355991257213327,
  0.950208137017567, 0.024895931491216494, 0.024895931491216494,
  0.49613589474104614, 0.4961358947410461, 0.007728210517907841,
  0.4696086896534919, 0.4696086896534919, 0.06078262069301621,
  0.23111028494908226, 0.23111028494908226, 0.5377794301018355,
  0.41447757027905463, 0.4144775702790546, 0.17104485944189085,
  0.11355991257213327, 0.11355991257213327, 0.7728801748557335,
  0.024895931491216494, 0.024895931491216494, 0.950208137017567,
  0.49613589474104614, 0.007728210517907841, 0.4961358947410461,
  0.4696086896534919, 0.06078262069301621, 0.4696086896534919,
  0.23111028494908226, 0.5377794301018355, 0.23111028494908226,
  0.41447757027905463, 0.17104485944189085, 0.4144775702790546,
  0.11355991257213327, 0.7728801748557335, 0.11355991257213327,
  0.024895931491216494, 0.950208137017567, 0.024895931491216494,
  0.6889333070396046, 0.01898800438375904, 0.2920786885766364,
  0.6355187156236324, 0.09773603106601653, 0.26674525331035115,
  0.8512338800096335, 0.021966344206529244, 0.1267997757838373,
  0.2920786885766363, 0.6889333070396046, 0.01898800438375904,
  0.26674525331035115, 0.6355187156236324, 0.09773603106601653,
  0.12679977578383728, 0.8512338800096335, 0.021966344206529244,
  0.018988004383758916, 0.2920786885766364, 0.6889333070396046,
  0.09773603106601647, 0.26674525331035115, 0.6355187156236324,
  0.02196634420652921, 0.1267997757838373, 0.8512338800096335,
  0.6889333070396046, 0.2920786885766364, 0.01898800438375904,
  0.6355187156236324, 0.26674525331035115, 0.09773603106601653,
  0.8512338800096335, 0.1267997757838373, 0.021966344206529244,
  0.018988004383758916, 0.6889333070396046, 0.2920786885766364,
  0.09773603106601647, 0.6355187156236324, 0.26674525331035115,
  0.02196634420652921, 0.8512338800096335, 0.1267997757838373,
  0.2920786885766363, 0.01898800438375904, 0.6889333070396046,
  0.26674525331035115, 0.09773603106601653, 0.6355187156236324,
  0.12679977578383728, 0.021966344206529244, 0.8512338800096335,
};
const double triangleRule13Weights[] = {
  0.05162264666429082,
  0.009941476361072588,
  0.03278124160372298,
  0.04606240959277825,
  0.0469470955421552,
  0.030903097975759793,
  0.008029399795258423,
  0.009941476361072588,
  0.03278124160372298,
  0.04606240959277825,
  0.0469470955421552,
  0.030903097975759793,
  0.008029399795258423,
  0.009941476361072588,
  0.03278124160372298,
  0.04606240959277825,
  0.0469470955421552,
  0.030903097975759793,
  0.008029399795258423,
  0.01812549864620088,
  0.037211960457261536,
  0.015393072683782177,
  0.01812549864620088,
  0.037211960457261536,
  0.015393072683782177,
  0.01812549864620088,
  0.037211960457261536,
  0.015393072683782177,
  0.01812549864620088,
  0.037211960457261536,
  0.015393072683782177,
  0.01812549864620088,
  0.037211960457261536,
  0.015393072683782177,
  0.01812549864620088,
  0.037211960457261536,
  0.015393072683782177,
};
const double triangleRule14Points[] = {
  0.16471056131909212, 0.41764471934045394, 0.41764471934045394,
  0.8764002338182546, 0.0617998830908727, 0.0617998830908727,
  0.4530449433823226, 0.2734775283088387, 0.2734775283088387,
  0.645588935174913, 0.1772055324125435, 0.1772055324125435,
  0.9612180775025978, 0.0193909612487011, 0.0193909612487011,
  0.022072179275642756, 0.4889639103621786, 0.4889639103621786,
  0.417644719340454, 0.41764471934045394, 0.16471056131909212,
  0.0617998830908727, 0.0617998830908727, 0.8764002338182546,
  0.27347752830883865, 0.2734775283088387, 0.4530449433823226,
  0.17720553241254344, 0.1772055324125435, 0.645588935174913,
  0.0193909612487011, 0.0193909612487011, 0.9612180775025978,
  0.48896391036217857, 0.4889639103621786, 0.022072179275642756,
  0.417644719340454, 0.16471056131909212, 0.41764471934045394,
  0.0617998830908727, 0.8764002338182546, 0.0617998830908727,
  0.27347752830883865, 0.4530449433823226, 0.2734775283088387,
  0.17720553241254344, 0.645588935174913, 0.1772055324125435,
  0.0193909612487011, 0.9612180775025978, 0.0193909612487011,
  0.48896391036217857, 0.022072179275642756, 0.4889639103621786,
  0.6869801678080878, 0.014646950055654471, 0.29837288213625773,
  0.5702222908466832, 0.09291624935697185, 0.336861459796345,
  0.7706085547749965, 0.05712475740364799, 0.17226668782135557,
  0.8797571713701711, 0.001268330932872076, 0.11897449769695682,
  0.2983728821362578, 0.6869801678080878, 0.014646950055654471,
  0.33686145979634496, 0.5702222908466832, 0.09291624935697185,
  0.17226668782135557, 0.7706085547749965, 0.05712475740364799,
  0.11897449769695678, 0.8797571713701712, 0.001268330932872076,
  0.014646950055654528, 0.29837288213625773, 0.6869801678080878,
  0.09291624935697174, 0.336861459796345, 0.5702222908466832,
  0.057124757403647974, 0.17226668782135557, 0.7706085547749965,
  0.0012683309328720416, 0.11897449769695682, 0.8797571713701712,
  0.6869801678080878, 0.29837288213625773, 0.014646950055654471,
  0.5702222908466832, 0.336861459796345, 0.09291624935697185,
  0.7706085547749965, 0.17226668782135557, 0.05712475740364799,
  0.8797571713701711, 0.11897449769695682, 0.001268330932872076,
  0.014646950055654528, 0.6869801678080878, 0.29837288213625773,
  0.09291624935697174, 0.5702222908466832, 0.336861459796345,
  0.057124757403647974, 0.7706085547749965, 0.17226668782135557,
  0.0012683309328720416, 0.8797571713701712, 0.11897449769695682,
  0.2983728821362578, 0.014646950055654471, 0.6869801678080878,
  0.33686145979634496, 0.09291624935697185, 0.5702222908466832,
  0.17226668782135557, 0.05712475740364799, 0.7706085547749965,
  0.11897449769695678, 0.001268330932872076, 0.8797571713701712,
};
const double triangleRule14Weights[] = {
  0.032788353544125355,
  0.014433699669776668,
  0.051774104507291585,
  0.04216258873699302,
  0.004923403602400082,
  0.021883581369428893,
  0.032788353544125355,
  0.014433699669776668,
  0.051774104507291585,
  0.04216258873699302,
  0.004923403602400082,
  0.021883581369428893,
  0.032788353544125355,
  0.014433699669776668,
  0.051774104507291585,
  0.04216258873699302,
  0.004923403602400082,
  0.021883581369428893,
  0.014436308113533842,
  0.038571510787060684,
  0.024665753212563677,
  0.005010228838500672,
  0.014436308113533842,
  0.038571510787060684,
  0.024665753212563677,
  0.005010228838500672,
  0.014436308113533842,
  0.038571510787060684,
  0.024665753212563677,
  0.005010228838500672,
  0.014436308113533842,
  0.038571510787060684,
  0.024665753212563677,
  0.005010228838500672,
  0.014436308113533842,
  0.038571510787060684,
  0.024665753212563677,
  0.005010228838500672,
  0.014436308113533842,
  0.038571510787060684,
  0.024665753212563677,
  0.005010228838500672,
};
const double triangleRule15Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.7400435401338442, 0.1299782299330779, 0.1299782299330779,
  0.07984610140588055, 0.4600769492970597, 0.4600769492970597,
  0.016628366739405598, 0.4916858166302972, 0.4916858166302972,
  0.5569353184097159, 0.22153234079514206, 0.22153234079514206,
  0.20613252518187886, 0.39693373740906057, 0.39693373740906057,
  0.8873161646077996, 0.0563419176961002, 0.0563419176961002,
  0.12997822993307784, 0.1299782299330779, 0.7400435401338442,
  0.4600769492970598, 0.4600769492970597, 0.07984610140588055,
  0.4916858166302972, 0.4916858166302972, 0.016628366739405598,
  0.22153234079514206, 0.22153234079514206, 0.5569353184097159,
  0.39693373740906057, 0.39693373740906057, 0.20613252518187886,
  0.0563419176961002, 0.0563419176961002, 0.8873161646077996,
  0.12997822993307784, 0.7400435401338442, 0.1299782299330779,
  0.4600769492970598, 0.07984610140588055, 0.4600769492970597,
  0.4916858166302972, 0.016628366739405598, 0.4916858166302972,
  0.22153234079514206, 0.5569353184097159, 0.22153234079514206,
  0.39693373740906057, 0.20613252518187886, 0.39693373740906057,
  0.0563419176961002, 0.8873161646077996, 0.0563419176961002,
  0.7330839951106168, 0.08459422148219181, 0.18232178340719132,
  0.8337725261484158, 0.016027089786345473, 0.15020038406523872,
  0.5792382424060449, 0.09765044243024235, 0.32311131516371266,
  0.6735980666116939, 0.018454251904633165, 0.3079476814836729,
  0.9608512354248769, 0.0011135352740137417, 0.03803522930110929,
  0.1823217834071913, 0.733083995110617, 0.08459422148219181,
  0.15020038406523872, 0.8337725261484158, 0.016027089786345473,
  0.3231113151637127, 0.5792382424060449, 0.09765044243024235,
  0.3079476814836729, 0.673598066611694, 0.018454251904633165,
  0.03803522930110925, 0.960851235424877, 0.0011135352740137417,
  0.08459422148219176, 0.18232178340719132, 0.733083995110617,
  0.016027089786345483, 0.15020038406523872, 0.8337725261484158,
  0.09765044243024246, 0.32311131516371266, 0.5792382424060449,
  0.018454251904633123, 0.3079476814836729, 0.673598066611694,
  0.0011135352740136994, 0.03803522930110929, 0.960851235424877,
  0.7330839951106168, 0.18232178340719132, 0.08459422148219181,
  0.8337725261484158, 0.15020038406523872, 0.016027089786345473,
  0.5792382424060449, 0.32311131516371266, 0.09765044243024235,
  0.6735980666116939, 0.3079476814836729, 0.018454251904633165,
  0.9608512354248769, 0.03803522930110929, 0.0011135352740137417,
  0.08459422148219176, 0.733083995110617, 0.18232178340719132,
  0.016027089786345483, 0.8337725261484158, 0.15020038406523872,
  0.09765044243024246, 0.5792382424060449, 0.32311131516371266,
  0.018454251904633123, 0.673598066611694, 0.3079476814836729,
  0.0011135352740136994, 0.960851235424877, 0.03803522930110929,
  0.1823217834071913, 0.08459422148219181, 0.733083995110617,
  0.15020038406523872, 0.016027089786345473, 0.8337725261484158,
  0.3231113151637127, 0.09765044243024235, 0.5792382424060449,
  0.3079476814836729, 0.018454251904633165, 0.673598066611694,
  0.03803522930110925, 0.0011135352740137417, 0.960851235424877,
};
const double triangleRule15Weights[] = {
  0.02973041974807132,
  0.0073975040670461,
  0.021594087936438452,
  0.0158322763500218,
  0.046287286105198076,
  0.046336041391207235,
  0.015084474247597068,
  0.0073975040670461,
  0.021594087936438452,
  0.0158322763500218,
  0.046287286105198076,
  0.046336041391207235,
  0.015084474247597068,
  0.0073975040670461,
  0.021594087936438452,
  0.0158322763500218,
  0.046287286105198076,
  0.046336041391207235,
  0.015084474247597068,
  0.024230008783125607,
  0.01122850429887806,
  0.03107522047051095,
  0.016436762092827895,
  0.0024752660145579163,
  0.024230008783125607,
  0.01122850429887806,
  0.03107522047051095,
  0.016436762092827895,
  0.0024752660145579163,
  0.024230008783125607,
  0.01122850429887806,
  0.03107522047051095,
  0.016436762092827895,
  0.0024752660145579163,
  0.024230008783125607,
  0.01122850429887806,
  0.03107522047051095,
  0.016436762092827895,
  0.0024752660145579163,
  0.024230008783125607,
  0.01122850429887806,
  0.03107522047051095,
  0.016436762092827895,
  0.0024752660145579163,
  0.024230008783125607,
  0.01122850429887806,
  0.03107522047051095,
  0.016436762092827895,
  0.0024752660145579163,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double triangleRule16Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.8666510555195233, 0.06667447224023837, 0.06667447224023837,
  0.5173566385972432, 0.24132168070137838, 0.24132168070137838,
  0.1744038080895527, 0.41279809595522365, 0.41279809595522365,
  0.6998725268259297, 0.15006373658703515, 0.15006373658703515,
  0.060903938006630076, 0.46954803099668496, 0.46954803099668496,
  0.965916741188563, 0.017041629405718517, 0.017041629405718517,
  0.06667447224023837, 0.06667447224023837, 0.8666510555195233,
  0.24132168070137838, 0.24132168070137838, 0.5173566385972432,
  0.41279809595522365, 0.41279809595522365, 0.1744038080895527,
  0.1500637365870352, 0.15006373658703515, 0.6998725268259297,
  0.46954803099668496, 0.46954803099668496, 0.060903938006630076,
  0.017041629405718517, 0.017041629405718517, 0.965916741188563,
  0.06667447224023837, 0.8666510555195233, 0.06667447224023837,
  0.24132168070137838, 0.5173566385972432, 0.24132168070137838,
  0.41279809595522365, 0.1744038080895527, 0.41279809595522365,
  0.1500637365870352, 0.6998725268259297, 0.15006373658703515,
  0.46954803099668496, 0.060903938006630076, 0.46954803099668496,
  0.017041629405718517, 0.965916741188563, 0.017041629405718517,
  0.5765655597692545, 0.009664954403660254, 0.41376948582708517,
  0.6655146084153338, 0.030305943355186365, 0.30417944822947973,
  0.8995779382011904, 0.010812972776103751, 0.08960908902270585,
  0.5967314670634687, 0.10665316053614844, 0.29661537240038294,
  0.7788823295056971, 0.051354315344013114, 0.16976335515028973,
  0.7822542773667971, 0.0036969427073556124, 0.21404877992584728,
  0.41376948582708517, 0.5765655597692546, 0.009664954403660254,
  0.30417944822947973, 0.6655146084153339, 0.030305943355186365,
  0.08960908902270581, 0.8995779382011905, 0.010812972776103751,
  0.29661537240038294, 0.5967314670634686, 0.10665316053614844,
  0.16976335515028973, 0.7788823295056971, 0.051354315344013114,
  0.21404877992584725, 0.7822542773667971, 0.0036969427073556124,
  0.00966495440366022, 0.41376948582708517, 0.5765655597692546,
  0.030305943355186327, 0.30417944822947973, 0.6655146084153339,
  0.010812972776103713, 0.08960908902270585, 0.8995779382011905,
  0.10665316053614848, 0.29661537240038294, 0.5967314670634686,
  0.051354315344013135, 0.16976335515028973, 0.7788823295056971,
  0.003696942707355655, 0.21404877992584728, 0.7822542773667971,
  0.5765655597692545, 0.41376948582708517, 0.009664954403660254,
  0.6655146084153338, 0.30417944822947973, 0.030305943355186365,
  0.8995779382011904, 0.08960908902270585, 0.010812972776103751,
  0.5967314670634687, 0.29661537240038294, 0.10665316053614844,
  0.7788823295056971, 0.16976335515028973, 0.051354315344013114,
  0.7822542773667971, 0.21404877992584728, 0.0036969427073556124,
  0.00966495440366022, 0.5765655597692546, 0.41376948582708517,
  0.030305943355186327, 0.6655146084153339, 0.30417944822947973,
  0.010812972776103713, 0.8995779382011905, 0.08960908902270585,
  0.10665316053614848, 0.5967314670634686, 0.29661537240038294,
  0.051354315344013135, 0.7788823295056971, 0.16976335515028973,
  0.003696942707355655, 0.7822542773667971, 0.21404877992584728,
  0.41376948582708517, 0.009664954403660254, 0.5765655597692546,
  0.30417944822947973, 0.030305943355186365, 0.6655146084153339,
  0.08960908902270581, 0.010812972776103751, 0.8995779382011905,
  0.29661537240038294, 0.10665316053614844, 0.5967314670634686,
  0.16976335515028973, 0.051354315344013114, 0.7788823295056971,
  0.21404877992584725, 0.0036969427073556124, 0.7822542773667971,
};
const double triangleRule16Weights[] = {
  0.046227910314191344,
  0.012425425595561009,
  0.04118404106979255,
  0.040985219786815366,
  0.02878349670274891,
  0.02709366946771045,
  0.003789135238264222,
  0.012425425595561009,
  0.04118404106979255,
  0.040985219786815366,
  0.02878349670274891,
  0.02709366946771045,
  0.003789135238264222,
  0.012425425595561009,
  0.04118404106979255,
  0.040985219786815366,
  0.02878349670274891,
  0.02709366946771045,
  0.003789135238264222,
  0.008182210553222139,
  0.013983607124653567,
  0.005751869970497159,
  0.031646061681983244,
  0.017653081047103284,
  0.0046146906397291345,
  0.008182210553222139,
  0.013983607124653567,
  0.005751869970497159,
  0.031646061681983244,
  0.017653081047103284,
  0.0046146906397291345,
  0.008182210553222139,
  0.013983607124653567,
  0.005751869970497159,
  0.031646061681983244,
  0.017653081047103284,
  0.0046146906397291345,
  0.008182210553222139,
  0.013983607124653567,
  0.005751869970497159,
  0.031646061681983244,
  0.017653081047103284,
  0.0046146906397291345,
  0.008182210553222139,
  0.013983607124653567,
  0.005751869970497159,
  0.031646061681983244,
  0.017653081047103284,
  0.0046146906397291345,
  0.008182210553222139,
  0.013983607124653567,
  0.005751869970497159,
  0.031646061681983244,
  0.017653081047103284,
  0.0046146906397291345,
};
const double triangleRule17Points[] = {
  0.16579311127680163, 0.4171034443615992, 0.4171034443615992,
  0.6392837674672587, 0.18035811626637066, 0.18035811626637066,
  0.42858699512682663, 0.2857065024365867, 0.2857065024365867,
  0.866691873040806, 0.06665406347959701, 0.06665406347959701,
  0.9704890166784919, 0.014755491660754072, 0.014755491660754072,
  0.06880425676221946, 0.46559787161889027, 0.46559787161889027,
  0.4171034443615992, 0.4171034443615992, 0.16579311127680163,
  0.18035811626637066, 0.18035811626637066, 0.6392837674672587,
  0.2857065024365867, 0.2857065024365867, 0.42858699512682663,
  0.06665406347959701, 0.06665406347959701, 0.866691873040806,
  0.014755491660754072, 0.014755491660754072, 0.9704890166784919,
  0.4655978716188902, 0.46559787161889027, 0.06880425676221946,
  0.4171034443615992, 0.16579311127680163, 0.4171034443615992,
  0.18035811626637066, 0.6392837674672587, 0.18035811626637066,
  0.2857065024365867, 0.42858699512682663, 0.2857065024365867,
  0.06665406347959701, 0.866691873040806, 0.06665406347959701,
  0.014755491660754072, 0.9704890166784919, 0.014755491660754072,
  0.4655978716188902, 0.06880425676221946, 0.46559787161889027,
  0.9159193532978169, 0.011575175903180683, 0.07250547079900238,
  0.571294867944684, 0.013229672760086951, 0.41547545929522905,
  0.7150722591106424, 0.013135870834002753, 0.27179187005535477,
  0.5432755795961597, 0.15750547792686992, 0.29921894247697034,
  0.6263690303864522, 0.06734937786736123, 0.3062815917461865,
  0.7532351459364581, 0.07804234056828245, 0.16872251349525944,
  0.824790070165088, 0.016017642362119337, 0.15919228747279268,
  0.07250547079900238, 0.9159193532978169, 0.011575175903180683,
  0.415475459295229, 0.5712948679446841, 0.013229672760086951,
  0.27179187005535477, 0.7150722591106424, 0.013135870834002753,
  0.29921894247697023, 0.5432755795961598, 0.15750547792686992,
  0.3062815917461865, 0.6263690303864522, 0.06734937786736123,
  0.16872251349525946, 0.7532351459364581, 0.07804234056828245,
  0.15919228747279268, 0.824790070165088, 0.016017642362119337,
  0.01157517590318069, 0.07250547079900238, 0.9159193532978169,
  0.013229672760086908, 0.41547545929522905, 0.5712948679446841,
  0.013135870834002805, 0.27179187005535477, 0.7150722591106424,
  0.15750547792686986, 0.29921894247697034, 0.5432755795961598,
  0.06734937786736128, 0.3062815917461865, 0.6263690303864522,
  0.07804234056828241, 0.16872251349525944, 0.7532351459364581,
  0.016017642362119333, 0.15919228747279268, 0.824790070165088,
  0.9159193532978169, 0.07250547079900238, 0.011575175903180683,
  0.571294867944684, 0.41547545929522905, 0.013229672760086951,
  0.7150722591106424, 0.27179187005535477, 0.013135870834002753,
  0.5432755795961597, 0.29921894247697034, 0.15750547792686992,
  0.6263690303864522, 0.3062815917461865, 0.06734937786736123,
  0.7532351459364581, 0.16872251349525944, 0.07804234056828245,
  0.824790070165088, 0.15919228747279268, 0.016017642362119337,
  0.01157517590318069, 0.9159193532978169, 0.07250547079900238,
  0.013229672760086908, 0.5712948679446841, 0.41547545929522905,
  0.013135870834002805, 0.7150722591106424, 0.27179187005535477,
  0.15750547792686986, 0.5432755795961598, 0.29921894247697034,
  0.06734937786736128, 0.6263690303864522, 0.3062815917461865,
  0.07804234056828241, 0.7532351459364581, 0.16872251349525944,
  0.016017642362119333, 0.824790070165088, 0.15919228747279268,
  0.07250547079900238, 0.011575175903180683, 0.9159193532978169,
  0.415475459295229, 0.013229672760086951, 0.5712948679446841,
  0.27179187005535477, 0.013135870834002753, 0.7150722591106424,
  0.29921894247697023, 0.15750547792686992, 0.5432755795961598,
  0.3062815917461865, 0.06734937786736123, 0.6263690303864522,
  0.16872251349525946, 0.07804234056828245, 0.7532351459364581,
  0.15919228747279268, 0.016017642362119337, 0.824790070165088,
};
const double triangleRule17Weights[] = {
  0.027310926528102106,
  0.026312630588017985,
  0.03771623715279528,
  0.012459000802305444,
  0.002773887577637642,
  0.02501945095049736,
  0.027310926528102106,
  0.026312630588017985,
  0.03771623715279528,
  0.012459000802305444,
  0.002773887577637642,
  0.02501945095049736,
  0.027310926528102106,
  0.026312630588017985,
  0.03771623715279528,
  0.012459000802305444,
  0.002773887577637642,
  0.02501945095049736,
  0.004584348401735868,
  0.010398439955839537,
  0.008692214501001192,
  0.02617162593533699,
  0.022487772546691067,
  0.02055789832045452,
  0.007978300205929593,
  0.004584348401735868,
  0.010398439955839537,
  0.008692214501001192,
  0.02617162593533699,
  0.022487772546691067,
  0.02055789832045452,
  0.007978300205929593,
  0.004584348401735868,
  0.010398439955839537,
  0.008692214501001192,
  0.02617162593533699,
  0.022487772546691067,
  0.02055789832045452,
  0.007978300205929593,
  0.004584348401735868,
  0.010398439955839537,
  0.008692214501001192,
  0.02617162593533699,
  0.022487772546691067,
  0.02055789832045452,
  0.007978300205929593,
  0.004584348401735868,
  0.010398439955839537,
  0.008692214501001192,
  0.02617162593533699,
  0.022487772546691067,
  0.02055789832045452,
  0.007978300205929593,
  0.004584348401735868,
  0.010398439955839537,
  0.008692214501001192,
  0.02617162593533699,
  0.022487772546691067,
  0.02055789832045452,
  0.007978300205929593,
};
const double triangleRule18Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.05016357735190857, 0.4749182113240457, 0.4749182113240457,
  0.6967229860547901, 0.15163850697260495, 0.15163850697260495,
  0.177865796248161, 0.4110671018759195, 0.4110671018759195,
  0.46877078018925156, 0.2656146099053742, 0.2656146099053742,
  0.9924821113178631, 0.0037589443410684376, 0.0037589443410684376,
  0.855122588865334, 0.072438705567333, 0.072438705567333,
  0.47491821132404577, 0.4749182113240457, 0.05016357735190857,
  0.15163850697260495, 0.15163850697260495, 0.6967229860547901,
  0.41106710187591955, 0.4110671018759195, 0.177865796248161,
  0.2656146099053742, 0.2656146099053742, 0.46877078018925156,
  0.003758944341068382, 0.0037589443410684376, 0.9924821113178631,
  0.072438705567333, 0.072438705567333, 0.855122588865334,
  0.47491821132404577, 0.05016357735190857, 0.4749182113240457,
  0.15163850697260495, 0.6967229860547901, 0.15163850697260495,
  0.41106710187591955, 0.177865796248161, 0.4110671018759195,
  0.2656146099053742, 0.46877078018925156, 0.2656146099053742,
  0.003758944341068382, 0.9924821113178631, 0.0037589443410684376,
  0.072438705567333, 0.855122588865334, 0.072438705567333,
  0.5245289252324956, 0.09042704035434063, 0.3850440344131637,
  0.9402249256838527, 0.012498932483495477, 0.04727614183265175,
  0.6439263069481049, 0.05401173533902428, 0.30206195771287075,
  0.7329888214065166, 0.010505018819241962, 0.2565061597742415,
  0.7553984164057089, 0.06612245802840343, 0.17847912556588763,
  0.5823597834782124, 0.14906691012577386, 0.2685733063960138,
  0.5772425066507145, 0.011691824674667157, 0.41106566867461836,
  0.8528896449496688, 0.014331524778941987, 0.1327788302713893,
  0.3850440344131636, 0.5245289252324957, 0.09042704035434063,
  0.04727614183265172, 0.9402249256838529, 0.012498932483495477,
  0.3020619577128708, 0.6439263069481049, 0.05401173533902428,
  0.2565061597742415, 0.7329888214065166, 0.010505018819241962,
  0.17847912556588763, 0.7553984164057089, 0.06612245802840343,
  0.26857330639601373, 0.5823597834782124, 0.14906691012577386,
  0.41106566867461836, 0.5772425066507145, 0.011691824674667157,
  0.13277883027138926, 0.8528896449496688, 0.014331524778941987,
  0.09042704035434057, 0.3850440344131637, 0.5245289252324957,
  0.012498932483495429, 0.04727614183265175, 0.9402249256838529,
  0.05401173533902437, 0.30206195771287075, 0.6439263069481049,
  0.01050501881924193, 0.2565061597742415, 0.7329888214065166,
  0.06612245802840344, 0.17847912556588763, 0.7553984164057089,
  0.14906691012577378, 0.2685733063960138, 0.5823597834782124,
  0.011691824674667117, 0.41106566867461836, 0.5772425066507145,
  0.014331524778941951, 0.1327788302713893, 0.8528896449496688,
  0.5245289252324956, 0.3850440344131637, 0.09042704035434063,
  0.9402249256838527, 0.04727614183265175, 0.012498932483495477,
  0.6439263069481049, 0.30206195771287075, 0.05401173533902428,
  0.7329888214065166, 0.2565061597742415, 0.010505018819241962,
  0.7553984164057089, 0.17847912556588763, 0.06612245802840343,
  0.5823597834782124, 0.2685733063960138, 0.14906691012577386,
  0.5772425066507145, 0.41106566867461836, 0.011691824674667157,
  0.8528896449496688, 0.1327788302713893, 0.014331524778941987,
  0.09042704035434057, 0.5245289252324957, 0.3850440344131637,
  0.012498932483495429, 0.9402249256838529, 0.04727614183265175,
  0.05401173533902437, 0.6439263069481049, 0.30206195771287075,
  0.01050501881924193, 0.7329888214065166, 0.2565061597742415,
  0.06612245802840344, 0.7553984164057089, 0.17847912556588763,
  0.14906691012577378, 0.5823597834782124, 0.2685733063960138,
  0.011691824674667117, 0.5772425066507145, 0.41106566867461836,
  0.014331524778941951, 0.8528896449496688, 0.1327788302713893,
  0.3850440344131636, 0.09042704035434063, 0.5245289252324957,
  0.04727614183265172, 0.012498932483495477, 0.9402249256838529,
  0.3020619577128708, 0.05401173533902428, 0.6439263069481049,
  0.2565061597742415, 0.010505018819241962, 0.7329888214065166,
  0.17847912556588763, 0.06612245802840343, 0.7553984164057089,
  0.26857330639601373, 0.14906691012577386, 0.5823597834782124,
  0.41106566867461836, 0.011691824674667157, 0.5772425066507145,
  0.13277883027138926, 0.014331524778941987, 0.8528896449496688,
};
const double triangleRule18Weights[] = {
  0.03074852123911586,
  0.013107027491738756,
  0.0203183388454584,
  0.0334719940598479,
  0.031116396602006133,
  0.0005320056169477806,
  0.013790286604766942,
  0.013107027491738756,
  0.0203183388454584,
  0.0334719940598479,
  0.031116396602006133,
  0.0005320056169477806,
  0.013790286604766942,
  0.013107027491738756,
  0.0203183388454584,
  0.0334719940598479,
  0.031116396602006133,
  0.0005320056169477806,
  0.013790286604766942,
  0.015328258194553142,
  0.004217516774744443,
  0.016365908413986566,
  0.007729835280006227,
  0.01691165391748008,
  0.02759288648857948,
  0.009586124474361505,
  0.007641704972719637,
  0.015328258194553142,
  0.004217516774744443,
  0.016365908413986566,
  0.007729835280006227,
  0.01691165391748008,
  0.02759288648857948,
  0.009586124474361505,
  0.007641704972719637,
  0.015328258194553142,
  0.004217516774744443,
  0.016365908413986566,
  0.007729835280006227,
  0.01691165391748008,
  0.02759288648857948,
  0.009586124474361505,
  0.007641704972719637,
  0.015328258194553142,
  0.004217516774744443,
  0.016365908413986566,
  0.007729835280006227,
  0.01691165391748008,
  0.02759288648857948,
  0.009586124474361505,
  0.007641704972719637,
  0.015328258194553142,
  0.004217516774744443,
  0.016365908413986566,
  0.007729835280006227,
  0.01691165391748008,
  0.02759288648857948,
  0.009586124474361505,
  0.007641704972719637,
  0.015328258194553142,
  0.004217516774744443,
  0.016365908413986566,
  0.007729835280006227,
  0.01691165391748008,
  0.02759288648857948,
  0.009586124474361505,
  0.007641704972719637,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double triangleRule19Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.8949474402917927, 0.05252627985410363, 0.05252627985410363,
  0.7771038885660024, 0.11144805571699878, 0.11144805571699878,
  0.9767219453441547, 0.011639027327922657, 0.011639027327922657,
  0.4896757336937503, 0.25516213315312486, 0.25516213315312486,
  0.19206056406722782, 0.4039697179663861, 0.4039697179663861,
  0.6436579878407449, 0.17817100607962755, 0.17817100607962755,
  0.08161122208634475, 0.4591943889568276, 0.4591943889568276,
  0.014975100268251551, 0.4925124498658742, 0.4925124498658742,
  0.05252627985410363, 0.05252627985410363, 0.8949474402917927,
  0.11144805571699878, 0.11144805571699878, 0.7771038885660024,
  0.011639027327922657, 0.011639027327922657, 0.9767219453441547,
  0.25516213315312486, 0.25516213315312486, 0.4896757336937503,
  0.40396971796638614, 0.4039697179663861, 0.19206056406722782,
  0.17817100607962755, 0.17817100607962755, 0.6436579878407449,
  0.4591943889568276, 0.4591943889568276, 0.08161122208634475,
  0.49251244986587417, 0.4925124498658742, 0.014975100268251551,
  0.05252627985410363, 0.8949474402917927, 0.05252627985410363,
  0.11144805571699878, 0.7771038885660024, 0.11144805571699878,
  0.011639027327922657, 0.9767219453441547, 0.011639027327922657,
  0.25516213315312486, 0.4896757336937503, 0.25516213315312486,
  0.40396971796638614, 0.19206056406722782, 0.4039697179663861,
  0.17817100607962755, 0.6436579878407449, 0.17817100607962755,
  0.4591943889568276, 0.08161122208634475, 0.4591943889568276,
  0.49251244986587417, 0.014975100268251551, 0.4925124498658742,
  0.8525725750765226, 0.005005142352350433, 0.1424222825711269,
  0.9301390385986208, 0.009777061438676854, 0.06008389996270236,
  0.8301568806048566, 0.039142449434608845, 0.13070066996053453,
  0.5593688070080342, 0.129312809767979, 0.31131838322398686,
  0.7040048688065315, 0.07456118930435514, 0.22143394188911344,
  0.60508575853531, 0.04088831446497813, 0.3540259269997119,
  0.7431822570856689, 0.014923638907438481, 0.24189410400689262,
  0.6333104818121876, 0.0020691038491023883, 0.36462041433871,
  0.14242228257112688, 0.8525725750765227, 0.005005142352350433,
  0.06008389996270236, 0.9301390385986208, 0.009777061438676854,
  0.13070066996053453, 0.8301568806048566, 0.039142449434608845,
  0.31131838322398686, 0.5593688070080342, 0.129312809767979,
  0.22143394188911347, 0.7040048688065313, 0.07456118930435514,
  0.3540259269997119, 0.60508575853531, 0.04088831446497813,
  0.2418941040068926, 0.7431822570856689, 0.014923638907438481,
  0.36462041433871006, 0.6333104818121875, 0.0020691038491023883,
  0.005005142352350389, 0.1424222825711269, 0.8525725750765227,
  0.009777061438676848, 0.06008389996270236, 0.9301390385986208,
  0.03914244943460887, 0.13070066996053453, 0.8301568806048566,
  0.129312809767979, 0.31131838322398686, 0.5593688070080342,
  0.07456118930435518, 0.22143394188911344, 0.7040048688065313,
  0.04088831446497809, 0.3540259269997119, 0.60508575853531,
  0.01492363890743853, 0.24189410400689262, 0.7431822570856689,
  0.002069103849102527, 0.36462041433871, 0.6333104818121875,
  0.8525725750765226, 0.1424222825711269, 0.005005142352350433,
  0.9301390385986208, 0.06008389996270236, 0.009777061438676854,
  0.8301568806048566, 0.13070066996053453, 0.039142449434608845,
  0.5593688070080342, 0.31131838322398686, 0.129312809767979,
  0.7040048688065315, 0.22143394188911344, 0.07456118930435514,
  0.60508575853531, 0.3540259269997119, 0.04088831446497813,
  0.7431822570856689, 0.24189410400689262, 0.014923638907438481,
  0.6333104818121876, 0.36462041433871, 0.0020691038491023883,
  0.005005142352350389, 0.8525725750765227, 0.1424222825711269,
  0.009777061438676848, 0.9301390385986208, 0.06008389996270236,
  0.03914244943460887, 0.8301568806048566, 0.13070066996053453,
  0.129312809767979, 0.5593688070080342, 0.31131838322398686,
  0.07456118930435518, 0.7040048688065313, 0.22143394188911344,
  0.04088831446497809, 0.60508575853531, 0.3540259269997119,
  0.01492363890743853, 0.7431822570856689, 0.24189410400689262,
  0.002069103849102527, 0.6333104818121875, 0.36462041433871,
  0.14242228257112688, 0.005005142352350433, 0.8525725750765227,
  0.06008389996270236, 0.009777061438676854, 0.9301390385986208,
  0.13070066996053453, 0.039142449434608845, 0.8301568806048566,
  0.31131838322398686, 0.129312809767979, 0.5593688070080342,
  0.22143394188911347, 0.07456118930435514, 0.7040048688065313,
  0.3540259269997119, 0.04088831446497813, 0.60508575853531,
  0.2418941040068926, 0.014923638907438481, 0.7431822570856689,
  0.36462041433871006, 0.0020691038491023883, 0.6333104818121875,
};
const double triangleRule19Weights[] = {
  0.034469160850905275,
  0.007109393622794947,
  0.015234956517004836,
  0.0017651924183085402,
  0.03175285458752998,
  0.03153735864523962,
  0.02465198105358483,
  0.022983570977123252,
  0.010321882182418864,
  0.007109393622794947,
  0.015234956517004836,
  0.0017651924183085402,
  0.03175285458752998,
  0.03153735864523962,
  0.02465198105358483,
  0.022983570977123252,
  0.010321882182418864,
  0.007109393622794947,
  0.015234956517004836,
  0.0017651924183085402,
  0.03175285458752998,
  0.03153735864523962,
  0.02465198105358483,
  0.022983570977123252,
  0.010321882182418864,
  0.0029256924878800715,
  0.0033273888405939045,
  0.009695519081624202,
  0.026346264707445364,
  0.018108074590430505,
  0.016102209460939428,
  0.00845592483909348,
  0.0032821375148397378,
  0.0029256924878800715,
  0.0033273888405939045,
  0.009695519081624202,
  0.026346264707445364,
  0.018108074590430505,
  0.016102209460939428,
  0.00845592483909348,
  0.0032821375148397378,
  0.0029256924878800715,
  0.0033273888405939045,
  0.009695519081624202,
  0.026346264707445364,
  0.018108074590430505,
  0.016102209460939428,
  0.00845592483909348,
  0.0032821375148397378,
  0.0029256924878800715,
  0.0033273888405939045,
  0.009695519081624202,
  0.026346264707445364,
  0.018108074590430505,
  0.016102209460939428,
  0.00845592483909348,
  0.0032821375148397378,
  0.0029256924878800715,
  0.0033273888405939045,
  0.009695519081624202,
  0.026346264707445364,
  0.018108074590430505,
  0.016102209460939428,
  0.00845592483909348,
  0.0032821375148397378,
  0.0029256924878800715,
  0.0033273888405939045,
  0.009695519081624202,
  0.026346264707445364,
  0.018108074590430505,
  0.016102209460939428,
  0.00845592483909348,
  0.0032821375148397378,
};
const double triangleRule20Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.6274100045109181, 0.18629499774454095, 0.18629499774454095,
  0.9253782388022305, 0.037310880598884766, 0.037310880598884766,
  0.047508776919002016, 0.476245611540499, 0.476245611540499,
  0.10889788608815043, 0.4455510569559248, 0.4455510569559248,
  0.4908414646533217, 0.25457926767333916, 0.25457926767333916,
  0.21314930436580026, 0.39342534781709987, 0.39342534781709987,
  0.9780477179432042, 0.01097614102839789, 0.01097614102839789,
  0.7812328065765706, 0.10938359671171471, 0.10938359671171471,
  0.18629499774454095, 0.18629499774454095, 0.6274100045109181,
  0.037310880598884766, 0.037310880598884766, 0.9253782388022305,
  0.47624561154049894, 0.476245611540499, 0.047508776919002016,
  0.4455510569559248, 0.4455510569559248, 0.10889788608815043,
  0.25457926767333916, 0.25457926767333916, 0.4908414646533217,
  0.3934253478170999, 0.39342534781709987, 0.21314930436580026,
  0.010976141028397945, 0.01097614102839789, 0.9780477179432042,
  0.10938359671171471, 0.10938359671171471, 0.7812328065765706,
  0.18629499774454095, 0.6274100045109181, 0.18629499774454095,
  0.037310880598884766, 0.9253782388022305, 0.037310880598884766,
  0.47624561154049894, 0.047508776919002016, 0.476245611540499,
  0.4455510569559248, 0.10889788608815043, 0.4455510569559248,
  0.25457926767333916, 0.4908414646533217, 0.25457926767333916,
  0.3934253478170999, 0.21314930436580026, 0.39342534781709987,
  0.010976141028397945, 0.9780477179432042, 0.01097614102839789,
  0.10938359671171471, 0.7812328065765706, 0.10938359671171471,
  0.9310544767839422, 0.004854937607623827, 0.06409058560843404,
  0.6781657378896355, 0.10622720472027006, 0.2156070573900944,
  0.8332955118382361, 0.007570780504696579, 0.15913370765706722,
  0.5423318041724281, 0.13980807199179993, 0.317860123835772,
  0.7549215028635474, 0.04656036490766434, 0.19851813222878817,
  0.8616840189364867, 0.038363684775374655, 0.09995229628813862,
  0.5701446928909734, 0.009831548292802588, 0.42002375881622406,
  0.6118777035474257, 0.05498747914298685, 0.33313481730958744,
  0.7086813757203236, 0.01073721285601111, 0.2805814114236652,
  0.06409058560843406, 0.9310544767839422, 0.004854937607623827,
  0.21560705739009445, 0.6781657378896355, 0.10622720472027006,
  0.15913370765706725, 0.8332955118382361, 0.007570780504696579,
  0.317860123835772, 0.5423318041724281, 0.13980807199179993,
  0.19851813222878822, 0.7549215028635474, 0.04656036490766434,
  0.09995229628813862, 0.8616840189364867, 0.038363684775374655,
  0.4200237588162241, 0.5701446928909732, 0.009831548292802588,
  0.3331348173095875, 0.6118777035474257, 0.05498747914298685,
  0.2805814114236652, 0.7086813757203236, 0.01073721285601111,
  0.004854937607623788, 0.06409058560843404, 0.9310544767839422,
  0.10622720472027014, 0.2156070573900944, 0.6781657378896355,
  0.007570780504696617, 0.15913370765706722, 0.8332955118382361,
  0.1398080719917999, 0.317860123835772, 0.5423318041724281,
  0.046560364907664464, 0.19851813222878817, 0.7549215028635474,
  0.03836368477537466, 0.09995229628813862, 0.8616840189364867,
  0.009831548292802639, 0.42002375881622406, 0.5701446928909732,
  0.05498747914298696, 0.33313481730958744, 0.6118777035474257,
  0.010737212856011147, 0.2805814114236652, 0.7086813757203236,
  0.9310544767839422, 0.06409058560843404, 0.004854937607623827,
  0.6781657378896355, 0.2156070573900944, 0.10622720472027006,
  0.8332955118382361, 0.15913370765706722, 0.007570780504696579,
  0.5423318041724281, 0.317860123835772, 0.13980807199179993,
  0.7549215028635474, 0.19851813222878817, 0.04656036490766434,
  0.8616840189364867, 0.09995229628813862, 0.038363684775374655,
  0.5701446928909734, 0.42002375881622406, 0.009831548292802588,
  0.6118777035474257, 0.33313481730958744, 0.05498747914298685,
  0.7086813757203236, 0.2805814114236652, 0.01073721285601111,
  0.004854937607623788, 0.9310544767839422, 0.06409058560843404,
  0.10622720472027014, 0.6781657378896355, 0.2156070573900944,
  0.007570780504696617, 0.8332955118382361, 0.15913370765706722,
  0.1398080719917999, 0.5423318041724281, 0.317860123835772,
  0.046560364907664464, 0.7549215028635474, 0.19851813222878817,
  0.03836368477537466, 0.8616840189364867, 0.09995229628813862,
  0.009831548292802639, 0.5701446928909732, 0.42002375881622406,
  0.05498747914298696, 0.6118777035474257, 0.33313481730958744,
  0.010737212856011147, 0.7086813757203236, 0.2805814114236652,
  0.06409058560843406, 0.004854937607623827, 0.9310544767839422,
  0.21560705739009445, 0.10622720472027006, 0.6781657378896355,
  0.15913370765706725, 0.007570780504696579, 0.8332955118382361,
  0.317860123835772, 0.13980807199179993, 0.5423318041724281,
  0.19851813222878822, 0.04656036490766434, 0.7549215028635474,
  0.09995229628813862, 0.038363684775374655, 0.8616840189364867,
  0.4200237588162241, 0.009831548292802588, 0.5701446928909732,
  0.3331348173095875, 0.05498747914298685, 0.6118777035474257,
  0.2805814114236652, 0.01073721285601111, 0.7086813757203236,
};
const double triangleRule20Weights[] = {
  0.027820221402906232,
  0.01834692594850583,
  0.0043225508213311555,
  0.014203650606816881,
  0.018904799866464896,
  0.028166402615040498,
  0.027576101258140917,
  0.00159768158213324,
  0.01566046155214907,
  0.01834692594850583,
  0.0043225508213311555,
  0.014203650606816881,
  0.018904799866464896,
  0.028166402615040498,
  0.027576101258140917,
  0.00159768158213324,
  0.01566046155214907,
  0.01834692594850583,
  0.0043225508213311555,
  0.014203650606816881,
  0.018904799866464896,
  0.028166402615040498,
  0.027576101258140917,
  0.00159768158213324,
  0.01566046155214907,
  0.002259739204251731,
  0.015445215644198462,
  0.004405794837116996,
  0.02338349146365547,
  0.01197279715790938,
  0.008291423055227716,
  0.007391363000510596,
  0.01733445113443867,
  0.007156400476915371,
  0.002259739204251731,
  0.015445215644198462,
  0.004405794837116996,
  0.02338349146365547,
  0.01197279715790938,
  0.008291423055227716,
  0.007391363000510596,
  0.01733445113443867,
  0.007156400476915371,
  0.002259739204251731,
  0.015445215644198462,
  0.004405794837116996,
  0.02338349146365547,
  0.01197279715790938,
  0.008291423055227716,
  0.007391363000510596,
  0.01733445113443867,
  0.007156400476915371,
  0.002259739204251731,
  0.015445215644198462,
  0.004405794837116996,
  0.02338349146365547,
  0.01197279715790938,
  0.008291423055227716,
  0.007391363000510596,
  0.01733445113443867,
  0.007156400476915371,
  0.002259739204251731,
  0.015445215644198462,
  0.004405794837116996,
  0.02338349146365547,
  0.01197279715790938,
  0.008291423055227716,
  0.007391363000510596,
  0.01733445113443867,
  0.007156400476915371,
  0.002259739204251731,
  0.015445215644198462,
  0.004405794837116996,
  0.02338349146365547,
  0.01197279715790938,
  0.008291423055227716,
  0.007391363000510596,
  0.01733445113443867,
  0.007156400476915371,
};
const double triangleRule21Points[] = {
  0.4021275293700348, 0.2989362353149826, 0.2989362353149826,
  0.005984249062628844, 0.4970078754686856, 0.4970078754686856,
  0.19276482690722974, 0.40361758654638513, 0.40361758654638513,
  0.762022844754561, 0.11898857762271953, 0.11898857762271953,
  0.6194225638174429, 0.19028871809127856, 0.19028871809127856,
  0.03680426269356685, 0.4815978686532166, 0.4815978686532166,
  0.10037441644927525, 0.4498127917753624, 0.4498127917753624,
  0.89274484890771, 0.053627575546145, 0.053627575546145,
  0.978515087134343, 0.010742456432828507, 0.010742456432828507,
  0.2989362353149826, 0.2989362353149826, 0.4021275293700348,
  0.4970078754686855, 0.4970078754686856, 0.005984249062628844,
  0.40361758654638513, 0.40361758654638513, 0.19276482690722974,
  0.11898857762271953, 0.11898857762271953, 0.762022844754561,
  0.19028871809127856, 0.19028871809127856, 0.6194225638174429,
  0.4815978686532165, 0.4815978686532166, 0.03680426269356685,
  0.4498127917753624, 0.4498127917753624, 0.10037441644927525,
  0.053627575546145057, 0.053627575546145, 0.89274484890771,
  0.010742456432828451, 0.010742456432828507, 0.978515087134343,
  0.2989362353149826, 0.4021275293700348, 0.2989362353149826,
  0.4970078754686855, 0.005984249062628844, 0.4970078754686856,
  0.40361758654638513, 0.19276482690722974, 0.40361758654638513,
  0.11898857762271953, 0.762022844754561, 0.11898857762271953,
  0.19028871809127856, 0.6194225638174429, 0.19028871809127856,
  0.4815978686532165, 0.03680426269356685, 0.4815978686532166,
  0.4498127917753624, 0.10037441644927525, 0.4498127917753624,
  0.053627575546145057, 0.89274484890771, 0.053627575546145,
  0.010742456432828451, 0.978515087134343, 0.010742456432828507,
  0.5055149445862437, 0.20529555933516153, 0.28918949607859473,
  0.7551948083705379, 0.006931809031468116, 0.23787338259799398,
  0.557355288799679, 0.12377940040549276, 0.31886531079482827,
  0.7291350120063786, 0.03899136262322033, 0.23187362537040096,
  0.857296629528919, 0.009536247529710598, 0.1331671229413703,
  0.6001398284888722, 0.05305219170121682, 0.34680797980991107,
  0.682942356735903, 0.10045802007411446, 0.21659962318998252,
  0.8217191264694079, 0.04945106556854055, 0.12882980796205154,
  0.6287919561081533, 0.010254635872924515, 0.3609534080189222,
  0.9339785312842042, 0.010301903643423904, 0.055719565072371954,
  0.2891894960785948, 0.5055149445862437, 0.20529555933516153,
  0.23787338259799395, 0.755194808370538, 0.006931809031468116,
  0.31886531079482827, 0.557355288799679, 0.12377940040549276,
  0.23187362537040102, 0.7291350120063786, 0.03899136262322033,
  0.13316712294137034, 0.857296629528919, 0.009536247529710598,
  0.34680797980991107, 0.6001398284888722, 0.05305219170121682,
  0.2165996231899825, 0.6829423567359031, 0.10045802007411446,
  0.12882980796205157, 0.8217191264694079, 0.04945106556854055,
  0.3609534080189222, 0.6287919561081533, 0.010254635872924515,
  0.05571956507237197, 0.9339785312842042, 0.010301903643423904,
  0.20529555933516153, 0.28918949607859473, 0.5055149445862437,
  0.006931809031468061, 0.23787338259799398, 0.755194808370538,
  0.12377940040549273, 0.31886531079482827, 0.557355288799679,
  0.03899136262322034, 0.23187362537040096, 0.7291350120063786,
  0.009536247529710717, 0.1331671229413703, 0.857296629528919,
  0.05305219170121678, 0.34680797980991107, 0.6001398284888722,
  0.10045802007411442, 0.21659962318998252, 0.6829423567359031,
  0.04945106556854051, 0.12882980796205154, 0.8217191264694079,
  0.010254635872924522, 0.3609534080189222, 0.6287919561081533,
  0.010301903643423871, 0.055719565072371954, 0.9339785312842042,
  0.5055149445862437, 0.28918949607859473, 0.20529555933516153,
  0.7551948083705379, 0.23787338259799398, 0.006931809031468116,
  0.557355288799679, 0.31886531079482827, 0.12377940040549276,
  0.7291350120063786, 0.23187362537040096, 0.03899136262322033,
  0.857296629528919, 0.1331671229413703, 0.009536247529710598,
  0.6001398284888722, 0.34680797980991107, 0.05305219170121682,
  0.682942356735903, 0.21659962318998252, 0.10045802007411446,
  0.8217191264694079, 0.12882980796205154, 0.04945106556854055,
  0.6287919561081533, 0.3609534080189222, 0.010254635872924515,
  0.9339785312842042, 0.055719565072371954, 0.010301903643423904,
  0.20529555933516153, 0.5055149445862437, 0.28918949607859473,
  0.006931809031468061, 0.755194808370538, 0.23787338259799398,
  0.12377940040549273, 0.557355288799679, 0.31886531079482827,
  0.03899136262322034, 0.7291350120063786, 0.23187362537040096,
  0.009536247529710717, 0.857296629528919, 0.1331671229413703,
  0.05305219170121678, 0.6001398284888722, 0.34680797980991107,
  0.10045802007411442, 0.6829423567359031, 0.21659962318998252,
  0.04945106556854051, 0.8217191264694079, 0.12882980796205154,
  0.010254635872924522, 0.6287919561081533, 0.3609534080189222,
  0.010301903643423871, 0.9339785312842042, 0.055719565072371954,
  0.2891894960785948, 0.20529555933516153, 0.5055149445862437,
  0.23787338259799395, 0.006931809031468116, 0.755194808370538,
  0.31886531079482827, 0.12377940040549276, 0.557355288799679,
  0.23187362537040102, 0.03899136262322033, 0.7291350120063786,
  0.13316712294137034, 0.009536247529710598, 0.857296629528919,
  0.34680797980991107, 0.05305219170121682, 0.6001398284888722,
  0.2165996231899825, 0.10045802007411446, 0.6829423567359031,
  0.12882980796205157, 0.04945106556854055, 0.8217191264694079,
  0.3609534080189222, 0.010254635872924515, 0.6287919561081533,
  0.05571956507237197, 0.010301903643423904, 0.9339785312842042,
};
const double triangleRule21Weights[] = {
  0.02145112192913234,
  0.004437829697065879,
  0.023000704653283865,
  0.013656032452230198,
  0.01945524186075071,
  0.012214410163384383,
  0.019614475227824023,
  0.0071520851012836515,
  0.0015086992723786893,
  0.02145112192913234,
  0.004437829697065879,
  0.023000704653283865,
  0.013656032452230198,
  0.01945524186075071,
  0.012214410163384383,
  0.019614475227824023,
  0.0071520851012836515,
  0.0015086992723786893,
  0.02145112192913234,
  0.004437829697065879,
  0.023000704653283865,
  0.013656032452230198,
  0.01945524186075071,
  0.012214410163384383,
  0.019614475227824023,
  0.0071520851012836515,
  0.0015086992723786893,
  0.017495416155763124,
  0.00420612028814973,
  0.018447484847932835,
  0.010469904185324846,
  0.004480813121901476,
  0.014500305918971022,
  0.015904036705427973,
  0.00981197182255041,
  0.006839884857934305,
  0.003265428584044085,
  0.017495416155763124,
  0.00420612028814973,
  0.018447484847932835,
  0.010469904185324846,
  0.004480813121901476,
  0.014500305918971022,
  0.015904036705427973,
  0.00981197182255041,
  0.006839884857934305,
  0.003265428584044085,
  0.017495416155763124,
  0.00420612028814973,
  0.018447484847932835,
  0.010469904185324846,
  0.004480813121901476,
  0.014500305918971022,
  0.015904036705427973,
  0.00981197182255041,
  0.006839884857934305,
  0.003265428584044085,
  0.017495416155763124,
  0.00420612028814973,
  0.018447484847932835,
  0.010469904185324846,
  0.004480813121901476,
  0.014500305918971022,
  0.015904036705427973,
  0.00981197182255041,
  0.006839884857934305,
  0.003265428584044085,
  0.017495416155763124,
  0.00420612028814973,
  0.018447484847932835,
  0.010469904185324846,
  0.004480813121901476,
  0.014500305918971022,
  0.015904036705427973,
  0.00981197182255041,
  0.006839884857934305,
  0.003265428584044085,
  0.017495416155763124,
  0.00420612028814973,
  0.018447484847932835,
  0.010469904185324846,
  0.004480813121901476,
  0.014500305918971022,
  0.015904036705427973,
  0.00981197182255041,
  0.006839884857934305,
  0.003265428584044085,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double triangleRule22Points[] = {
  0.22963095074539575, 0.3851845246273021, 0.3851845246273021,
  0.08446117726465585, 0.4577694113676721, 0.4577694113676721,
  0.4108834819400997, 0.29455825902995014, 0.29455825902995014,
  0.622978952739432, 0.18851052363028398, 0.18851052363028398,
  0.15603622241293014, 0.42198188879353493, 0.42198188879353493,
  0.007677643180582727, 0.49616117840970864, 0.49616117840970864,
  0.9417830586583849, 0.029108470670807574, 0.029108470670807574,
  0.76913692356159, 0.11543153821920499, 0.11543153821920499,
  0.3851845246273021, 0.3851845246273021, 0.22963095074539575,
  0.457769411367672, 0.4577694113676721, 0.08446117726465585,
  0.29455825902995014, 0.29455825902995014, 0.4108834819400997,
  0.18851052363028398, 0.18851052363028398, 0.622978952739432,
  0.42198188879353493, 0.42198188879353493, 0.15603622241293014,
  0.49616117840970864, 0.49616117840970864, 0.007677643180582727,
  0.029108470670807574, 0.029108470670807574, 0.9417830586583849,
  0.11543153821920504, 0.11543153821920499, 0.76913692356159,
  0.3851845246273021, 0.22963095074539575, 0.3851845246273021,
  0.457769411367672, 0.08446117726465585, 0.4577694113676721,
  0.29455825902995014, 0.4108834819400997, 0.29455825902995014,
  0.18851052363028398, 0.622978952739432, 0.18851052363028398,
  0.42198188879353493, 0.15603622241293014, 0.42198188879353493,
  0.49616117840970864, 0.007677643180582727, 0.49616117840970864,
  0.029108470670807574, 0.9417830586583849, 0.029108470670807574,
  0.11543153821920504, 0.76913692356159, 0.11543153821920499,
  0.922281548310974, 0.007876282221582374, 0.06984216946744362,
  0.8648488844852564, 0.04475228434833587, 0.09039883116640775,
  0.5503830012785775, 0.038275234700863824, 0.4113417640205587,
  0.5651468190056221, 0.10274707598693139, 0.3321061050074464,
  0.630023478332822, 0.007400241234710751, 0.36257628043246726,
  0.5188518779166111, 0.19108129796672008, 0.29006682411666884,
  0.6680765517823724, 0.04399164539345585, 0.28793180282417186,
  0.6745231247723869, 0.10868994186267199, 0.21678693336494115,
  0.8449815687515108, 0.009144711374964054, 0.14587371987352518,
  0.7754476410608586, 0.048254924114641384, 0.17629743482450005,
  0.7468454447123217, 0.009163909248185229, 0.24399064603949305,
  0.9802672139581127, 0.0017984649889483744, 0.017934321052938986,
  0.0698421694674436, 0.9222815483109741, 0.007876282221582374,
  0.09039883116640779, 0.8648488844852563, 0.04475228434833587,
  0.41134176402055866, 0.5503830012785775, 0.038275234700863824,
  0.3321061050074463, 0.5651468190056222, 0.10274707598693139,
  0.36257628043246726, 0.630023478332822, 0.007400241234710751,
  0.29006682411666884, 0.5188518779166111, 0.19108129796672008,
  0.28793180282417197, 0.6680765517823722, 0.04399164539345585,
  0.21678693336494115, 0.6745231247723869, 0.10868994186267199,
  0.14587371987352515, 0.8449815687515108, 0.009144711374964054,
  0.1762974348245, 0.7754476410608586, 0.048254924114641384,
  0.24399064603949305, 0.7468454447123217, 0.009163909248185229,
  0.017934321052939017, 0.9802672139581126, 0.0017984649889483744,
  0.00787628222158232, 0.06984216946744362, 0.9222815483109741,
  0.04475228434833589, 0.09039883116640775, 0.8648488844852563,
  0.03827523470086369, 0.4113417640205587, 0.5503830012785775,
  0.10274707598693134, 0.3321061050074464, 0.5651468190056222,
  0.007400241234710725, 0.36257628043246726, 0.630023478332822,
  0.19108129796672002, 0.29006682411666884, 0.5188518779166111,
  0.0439916453934559, 0.28793180282417186, 0.6680765517823722,
  0.108689941862672, 0.21678693336494115, 0.6745231247723869,
  0.009144711374964087, 0.14587371987352518, 0.8449815687515108,
  0.04825492411464127, 0.17629743482450005, 0.7754476410608586,
  0.00916390924818522, 0.24399064603949305, 0.7468454447123217,
  0.0017984649889484228, 0.017934321052938986, 0.9802672139581126,
  0.922281548310974, 0.06984216946744362, 0.007876282221582374,
  0.8648488844852564, 0.09039883116640775, 0.04475228434833587,
  0.5503830012785775, 0.4113417640205587, 0.038275234700863824,
  0.5651468190056221, 0.3321061050074464, 0.10274707598693139,
  0.630023478332822, 0.36257628043246726, 0.007400241234710751,
  0.5188518779166111, 0.29006682411666884, 0.19108129796672008,
  0.6680765517823724, 0.28793180282417186, 0.04399164539345585,
  0.6745231247723869, 0.21678693336494115, 0.10868994186267199,
  0.8449815687515108, 0.14587371987352518, 0.009144711374964054,
  0.7754476410608586, 0.17629743482450005, 0.048254924114641384,
  0.7468454447123217, 0.24399064603949305, 0.009163909248185229,
  0.9802672139581127, 0.017934321052938986, 0.0017984649889483744,
  0.00787628222158232, 0.9222815483109741, 0.06984216946744362,
  0.04475228434833589, 0.8648488844852563, 0.09039883116640775,
  0.03827523470086369, 0.5503830012785775, 0.4113417640205587,
  0.10274707598693134, 0.5651468190056222, 0.3321061050074464,
  0.007400241234710725, 0.630023478332822, 0.36257628043246726,
  0.19108129796672002, 0.5188518779166111, 0.29006682411666884,
  0.0439916453934559, 0.6680765517823722, 0.28793180282417186,
  0.108689941862672, 0.6745231247723869, 0.21678693336494115,
  0.009144711374964087, 0.8449815687515108, 0.14587371987352518,
  0.04825492411464127, 0.7754476410608586, 0.17629743482450005,
  0.00916390924818522, 0.7468454447123217, 0.24399064603949305,
  0.0017984649889484228, 0.9802672139581126, 0.017934321052938986,
  0.0698421694674436, 0.007876282221582374, 0.9222815483109741,
  0.09039883116640779, 0.04475228434833587, 0.8648488844852563,
  0.41134176402055866, 0.038275234700863824, 0.5503830012785775,
  0.3321061050074463, 0.10274707598693139, 0.5651468190056222,
  0.36257628043246726, 0.007400241234710751, 0.630023478332822,
  0.29006682411666884, 0.19108129796672008, 0.5188518779166111,
  0.28793180282417197, 0.04399164539345585, 0.6680765517823722,
  0.21678693336494115, 0.10868994186267199, 0.6745231247723869,
  0.14587371987352515, 0.009144711374964054, 0.8449815687515108,
  0.1762974348245, 0.048254924114641384, 0.7754476410608586,
  0.24399064603949305, 0.009163909248185229, 0.7468454447123217,
  0.017934321052939017, 0.0017984649889483744, 0.9802672139581126,
};
const double triangleRule22Weights[] = {
  0.013493083883610662,
  0.013861399524234192,
  0.021075763957452184,
  0.01602129912514889,
  0.018853092553841287,
  0.005289339665984418,
  0.0035691091658563764,
  0.014415713128104602,
  0.013493083883610662,
  0.013861399524234192,
  0.021075763957452184,
  0.01602129912514889,
  0.018853092553841287,
  0.005289339665984418,
  0.0035691091658563764,
  0.014415713128104602,
  0.013493083883610662,
  0.013861399524234192,
  0.021075763957452184,
  0.01602129912514889,
  0.018853092553841287,
  0.005289339665984418,
  0.0035691091658563764,
  0.014415713128104602,
  0.0025954384742312778,
  0.007517577817788376,
  0.01119731347196277,
  0.01771909348951022,
  0.0049042603975569645,
  0.02170641955550896,
  0.011662222867343003,
  0.015710162622570318,
  0.004106687071575556,
  0.010563584967746897,
  0.0050540768975846015,
  0.0006404285311714258,
  0.0025954384742312778,
  0.007517577817788376,
  0.01119731347196277,
  0.01771909348951022,
  0.0049042603975569645,
  0.02170641955550896,
  0.011662222867343003,
  0.015710162622570318,
  0.004106687071575556,
  0.010563584967746897,
  0.0050540768975846015,
  0.0006404285311714258,
  0.0025954384742312778,
  0.007517577817788376,
  0.01119731347196277,
  0.01771909348951022,
  0.0049042603975569645,
  0.02170641955550896,
  0.011662222867343003,
  0.015710162622570318,
  0.004106687071575556,
  0.010563584967746897,
  0.0050540768975846015,
  0.0006404285311714258,
  0.0025954384742312778,
  0.007517577817788376,
  0.01119731347196277,
  0.01771909348951022,
  0.0049042603975569645,
  0.02170641955550896,
  0.011662222867343003,
  0.015710162622570318,
  0.004106687071575556,
  0.010563584967746897,
  0.0050540768975846015,
  0.0006404285311714258,
  0.0025954384742312778,
  0.007517577817788376,
  0.01119731347196277,
  0.01771909348951022,
  0.0049042603975569645,
  0.02170641955550896,
  0.011662222867343003,
  0.015710162622570318,
  0.004106687071575556,
  0.010563584967746897,
  0.0050540768975846015,
  0.0006404285311714258,
  0.0025954384742312778,
  0.007517577817788376,
  0.01119731347196277,
  0.01771909348951022,
  0.0049042603975569645,
  0.02170641955550896,
  0.011662222867343003,
  0.015710162622570318,
  0.004106687071575556,
  0.010563584967746897,
  0.0050540768975846015,
  0.0006404285311714258,
};
const double triangleRule23Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.9219854624859356, 0.0390072687570322, 0.0390072687570322,
  0.039342245325382996, 0.4803288773373085, 0.4803288773373085,
  0.8263179035847336, 0.08684104820763322, 0.08684104820763322,
  0.21135298797691693, 0.39432350601154154, 0.39432350601154154,
  0.46749736424550536, 0.2662513178772473, 0.2662513178772473,
  0.7257412253767046, 0.1371293873116477, 0.1371293873116477,
  0.002081137580827397, 0.4989594312095863, 0.4989594312095863,
  0.11061511574454497, 0.4446924421277275, 0.4446924421277275,
  0.6025003872069274, 0.19874980639653628, 0.19874980639653628,
  0.9819671195888031, 0.009016440205598442, 0.009016440205598442,
  0.0390072687570322, 0.0390072687570322, 0.9219854624859356,
  0.48032887733730845, 0.4803288773373085, 0.039342245325382996,
  0.08684104820763316, 0.08684104820763322, 0.8263179035847336,
  0.39432350601154154, 0.39432350601154154, 0.21135298797691693,
  0.2662513178772473, 0.2662513178772473, 0.46749736424550536,
  0.1371293873116477, 0.1371293873116477, 0.7257412253767046,
  0.4989594312095863, 0.4989594312095863, 0.002081137580827397,
  0.4446924421277275, 0.4446924421277275, 0.11061511574454497,
  0.19874980639653628, 0.19874980639653628, 0.6025003872069274,
  0.009016440205598442, 0.009016440205598442, 0.9819671195888031,
  0.0390072687570322, 0.9219854624859356, 0.0390072687570322,
  0.48032887733730845, 0.039342245325382996, 0.4803288773373085,
  0.08684104820763316, 0.8263179035847336, 0.08684104820763322,
  0.39432350601154154, 0.21135298797691693, 0.39432350601154154,
  0.2662513178772473, 0.46749736424550536, 0.2662513178772473,
  0.1371293873116477, 0.7257412253767046, 0.1371293873116477,
  0.4989594312095863, 0.002081137580827397, 0.4989594312095863,
  0.4446924421277275, 0.11061511574454497, 0.4446924421277275,
  0.19874980639653628, 0.6025003872069274, 0.19874980639653628,
  0.009016440205598442, 0.9819671195888031, 0.009016440205598442,
  0.8166259474208892, 0.02387025365435361, 0.15950379892475722,
  0.8807088179167909, 0.005189821760844536, 0.11410136032236454,
  0.8717190926395587, 0.0327410291887064, 0.0955398781717349,
  0.6863901320923317, 0.0024475998559663793, 0.31116226805170194,
  0.7856574783566395, 0.008725289585308535, 0.20561723205805207,
  0.9455758306400303, 0.007162539910244482, 0.0472616294497253,
  0.5729634522431619, 0.068526954187213, 0.3585095935696251,
  0.6577888986377031, 0.10172832932728422, 0.2404827720350127,
  0.7687161216332605, 0.05835157523751544, 0.17293230312922397,
  0.5288655369406456, 0.1548301554055162, 0.3163043076538381,
  0.5874824534670472, 0.014758969729945169, 0.39775857680300764,
  0.688212121993365, 0.03299370819253279, 0.27879416981410227,
  0.1595037989247572, 0.8166259474208892, 0.02387025365435361,
  0.11410136032236451, 0.880708817916791, 0.005189821760844536,
  0.09553987817173493, 0.8717190926395587, 0.0327410291887064,
  0.311162268051702, 0.6863901320923316, 0.0024475998559663793,
  0.20561723205805205, 0.7856574783566395, 0.008725289585308535,
  0.04726162944972534, 0.9455758306400301, 0.007162539910244482,
  0.3585095935696251, 0.5729634522431619, 0.068526954187213,
  0.24048277203501267, 0.6577888986377031, 0.10172832932728422,
  0.17293230312922403, 0.7687161216332605, 0.05835157523751544,
  0.3163043076538381, 0.5288655369406456, 0.1548301554055162,
  0.39775857680300764, 0.5874824534670472, 0.014758969729945169,
  0.2787941698141022, 0.688212121993365, 0.03299370819253279,
  0.02387025365435358, 0.15950379892475722, 0.8166259474208892,
  0.005189821760844482, 0.11410136032236454, 0.880708817916791,
  0.03274102918870636, 0.0955398781717349, 0.8717190926395587,
  0.0024475998559665424, 0.31116226805170194, 0.6863901320923316,
  0.008725289585308493, 0.20561723205805207, 0.7856574783566395,
  0.007162539910244514, 0.0472616294497253, 0.9455758306400301,
  0.068526954187213, 0.3585095935696251, 0.5729634522431619,
  0.10172832932728426, 0.2404827720350127, 0.6577888986377031,
  0.05835157523751544, 0.17293230312922397, 0.7687161216332605,
  0.15483015540551626, 0.3163043076538381, 0.5288655369406456,
  0.01475896972994517, 0.39775857680300764, 0.5874824534670472,
  0.03299370819253267, 0.27879416981410227, 0.688212121993365,
  0.8166259474208892, 0.15950379892475722, 0.02387025365435361,
  0.8807088179167909, 0.11410136032236454, 0.005189821760844536,
  0.8717190926395587, 0.0955398781717349, 0.0327410291887064,
  0.6863901320923317, 0.31116226805170194, 0.0024475998559663793,
  0.7856574783566395, 0.20561723205805207, 0.008725289585308535,
  0.9455758306400303, 0.0472616294497253, 0.007162539910244482,
  0.5729634522431619, 0.3585095935696251, 0.068526954187213,
  0.6577888986377031, 0.2404827720350127, 0.10172832932728422,
  0.7687161216332605, 0.17293230312922397, 0.05835157523751544,
  0.5288655369406456, 0.3163043076538381, 0.1548301554055162,
  0.5874824534670472, 0.39775857680300764, 0.014758969729945169,
  0.688212121993365, 0.27879416981410227, 0.03299370819253279,
  0.02387025365435358, 0.8166259474208892, 0.15950379892475722,
  0.005189821760844482, 0.880708817916791, 0.11410136032236454,
  0.03274102918870636, 0.8717190926395587, 0.0955398781717349,
  0.0024475998559665424, 0.6863901320923316, 0.31116226805170194,
  0.008725289585308493, 0.7856574783566395, 0.20561723205805207,
  0.007162539910244514, 0.9455758306400301, 0.0472616294497253,
  0.068526954187213, 0.5729634522431619, 0.3585095935696251,
  0.10172832932728426, 0.6577888986377031, 0.2404827720350127,
  0.05835157523751544, 0.7687161216332605, 0.17293230312922397,
  0.15483015540551626, 0.5288655369406456, 0.3163043076538381,
  0.01475896972994517, 0.5874824534670472, 0.39775857680300764,
  0.03299370819253267, 0.688212121993365, 0.27879416981410227,
  0.1595037989247572, 0.02387025365435361, 0.8166259474208892,
  0.11410136032236451, 0.005189821760844536, 0.880708817916791,
  0.09553987817173493, 0.0327410291887064, 0.8717190926395587,
  0.311162268051702, 0.0024475998559663793, 0.6863901320923316,
  0.20561723205805205, 0.008725289585308535, 0.7856574783566395,
  0.04726162944972534, 0.007162539910244482, 0.9455758306400301,
  0.3585095935696251, 0.068526954187213, 0.5729634522431619,
  0.24048277203501267, 0.10172832932728422, 0.6577888986377031,
  0.17293230312922403, 0.05835157523751544, 0.7687161216332605,
  0.3163043076538381, 0.1548301554055162, 0.5288655369406456,
  0.39775857680300764, 0.014758969729945169, 0.5874824534670472,
  0.2787941698141022, 0.03299370819253279, 0.688212121993365,
};
const double triangleRule23Weights[] = {
  0.02525306032303621,
  0.003915740259032936,
  0.01139788926780076,
  0.008959917025513542,
  0.023674608463128022,
  0.023807862887499764,
  0.01455944939274175,
  0.0024075446041814095,
  0.018951950669338885,
  0.019935277880105025,
  0.001065361232829315,
  0.003915740259032936,
  0.01139788926780076,
  0.008959917025513542,
  0.023674608463128022,
  0.023807862887499764,
  0.01455944939274175,
  0.0024075446041814095,
  0.018951950669338885,
  0.019935277880105025,
  0.001065361232829315,
  0.003915740259032936,
  0.01139788926780076,
  0.008959917025513542,
  0.023674608463128022,
  0.023807862887499764,
  0.01455944939274175,
  0.0024075446041814095,
  0.018951950669338885,
  0.019935277880105025,
  0.001065361232829315,
  0.002528166055382263,
  0.0022250197297245147,
  0.005328030431194785,
  0.0022811036762558344,
  0.004114750344416092,
  0.0019525913278907261,
  0.014981113393199167,
  0.016121241637017152,
  0.010470256493130067,
  0.02084439585896881,
  0.007097778834521825,
  0.010175574656707037,
  0.002528166055382263,
  0.0022250197297245147,
  0.005328030431194785,
  0.0022811036762558344,
  0.004114750344416092,
  0.0019525913278907261,
  0.014981113393199167,
  0.016121241637017152,
  0.010470256493130067,
  0.02084439585896881,
  0.007097778834521825,
  0.010175574656707037,
  0.002528166055382263,
  0.0022250197297245147,
  0.005328030431194785,
  0.0022811036762558344,
  0.004114750344416092,
  0.0019525913278907261,
  0.014981113393199167,
  0.016121241637017152,
  0.010470256493130067,
  0.02084439585896881,
  0.007097778834521825,
  0.010175574656707037,
  0.002528166055382263,
  0.0022250197297245147,
  0.005328030431194785,
  0.0022811036762558344,
  0.004114750344416092,
  0.0019525913278907261,
  0.014981113393199167,
  0.016121241637017152,
  0.010470256493130067,
  0.02084439585896881,
  0.007097778834521825,
  0.010175574656707037,
  0.002528166055382263,
  0.0022250197297245147,
  0.005328030431194785,
  0.0022811036762558344,
  0.004114750344416092,
  0.0019525913278907261,
  0.014981113393199167,
  0.016121241637017152,
  0.010470256493130067,
  0.02084439585896881,
  0.007097778834521825,
  0.010175574656707037,
  0.002528166055382263,
  0.0022250197297245147,
  0.005328030431194785,
  0.0022811036762558344,
  0.004114750344416092,
  0.0019525913278907261,
  0.014981113393199167,
  0.016121241637017152,
  0.010470256493130067,
  0.02084439585896881,
  0.007097778834521825,
  0.010175574656707037,
};
const double triangleRule24Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.16221805017879443, 0.4188909749106028, 0.4188909749106028,
  0.6752787325661471, 0.16236063371692644, 0.16236063371692644,
  0.9180287419977657, 0.04098562900111713, 0.04098562900111713,
  0.9865374582242231, 0.006731270887888441, 0.006731270887888441,
  0.007489444648529742, 0.49625527767573513, 0.49625527767573513,
  0.4715373691234548, 0.2642313154382726, 0.2642313154382726,
  0.03877487641499355, 0.4806125617925032, 0.4806125617925032,
  0.8073430088015694, 0.0963284955992153, 0.0963284955992153,
  0.24929414659582738, 0.3753529267020863, 0.3753529267020863,
  0.4188909749106028, 0.4188909749106028, 0.16221805017879443,
  0.16236063371692644, 0.16236063371692644, 0.6752787325661471,
  0.04098562900111713, 0.04098562900111713, 0.9180287419977657,
  0.006731270887888385, 0.006731270887888441, 0.9865374582242231,
  0.4962552776757352, 0.49625527767573513, 0.007489444648529742,
  0.2642313154382726, 0.2642313154382726, 0.4715373691234548,
  0.4806125617925032, 0.4806125617925032, 0.03877487641499355,
  0.0963284955992153, 0.0963284955992153, 0.8073430088015694,
  0.3753529267020863, 0.3753529267020863, 0.24929414659582738,
  0.4188909749106028, 0.16221805017879443, 0.4188909749106028,
  0.16236063371692644, 0.6752787325661471, 0.16236063371692644,
  0.04098562900111713, 0.9180287419977657, 0.04098562900111713,
  0.006731270887888385, 0.9865374582242231, 0.006731270887888441,
  0.4962552776757352, 0.007489444648529742, 0.49625527767573513,
  0.2642313154382726, 0.4715373691234548, 0.2642313154382726,
  0.4806125617925032, 0.03877487641499355, 0.4806125617925032,
  0.0963284955992153, 0.8073430088015694, 0.0963284955992153,
  0.3753529267020863, 0.24929414659582738, 0.3753529267020863,
  0.5881529574639623, 0.17036728246244368, 0.241479760073594,
  0.5012643952150376, 0.169759795860736, 0.3289758089242264,
  0.8685143643990995, 0.03831822582101938, 0.09316740977988115,
  0.5128232386790481, 0.09265648152075752, 0.39452027980019433,
  0.7961338693570472, 0.041188714248475373, 0.16267741639447741,
  0.7068400808109625, 0.03957090497015804, 0.25358901421887947,
  0.5991550585073127, 0.038592700174896126, 0.36225224131779127,
  0.6238424605572401, 0.09453496173659899, 0.28162257770616084,
  0.6093393403750466, 0.007387994632294238, 0.3832726649926592,
  0.7187036443214267, 0.007546003162312815, 0.2737503525162605,
  0.8986440987448518, 0.007234558457782137, 0.09412134279736603,
  0.724037578585869, 0.09556626952736523, 0.18039615188676572,
  0.8172747318363464, 0.007987921880847964, 0.17473734628280568,
  0.9546336170785, 0.008074910870208776, 0.03729147205129122,
  0.24147976007359395, 0.5881529574639623, 0.17036728246244368,
  0.3289758089242264, 0.5012643952150376, 0.169759795860736,
  0.09316740977988114, 0.8685143643990995, 0.03831822582101938,
  0.39452027980019433, 0.5128232386790481, 0.09265648152075752,
  0.16267741639447741, 0.7961338693570472, 0.041188714248475373,
  0.25358901421887947, 0.7068400808109625, 0.03957090497015804,
  0.3622522413177912, 0.5991550585073127, 0.038592700174896126,
  0.28162257770616084, 0.6238424605572401, 0.09453496173659899,
  0.3832726649926592, 0.6093393403750466, 0.007387994632294238,
  0.27375035251626045, 0.7187036443214267, 0.007546003162312815,
  0.09412134279736606, 0.8986440987448518, 0.007234558457782137,
  0.18039615188676572, 0.724037578585869, 0.09556626952736523,
  0.17473734628280568, 0.8172747318363464, 0.007987921880847964,
  0.03729147205129124, 0.9546336170785, 0.008074910870208776,
  0.1703672824624436, 0.241479760073594, 0.5881529574639623,
  0.16975979586073597, 0.3289758089242264, 0.5012643952150376,
  0.0383182258210194, 0.09316740977988115, 0.8685143643990995,
  0.09265648152075756, 0.39452027980019433, 0.5128232386790481,
  0.04118871424847537, 0.16267741639447741, 0.7961338693570472,
  0.03957090497015803, 0.25358901421887947, 0.7068400808109625,
  0.03859270017489602, 0.36225224131779127, 0.5991550585073127,
  0.09453496173659903, 0.28162257770616084, 0.6238424605572401,
  0.007387994632294226, 0.3832726649926592, 0.6093393403750466,
  0.007546003162312687, 0.2737503525162605, 0.7187036443214267,
  0.007234558457782092, 0.09412134279736603, 0.8986440987448518,
  0.09556626952736524, 0.18039615188676572, 0.724037578585869,
  0.007987921880847959, 0.17473734628280568, 0.8172747318363464,
  0.008074910870208729, 0.03729147205129122, 0.9546336170785,
  0.5881529574639623, 0.241479760073594, 0.17036728246244368,
  0.5012643952150376, 0.3289758089242264, 0.169759795860736,
  0.8685143643990995, 0.09316740977988115, 0.03831822582101938,
  0.5128232386790481, 0.39452027980019433, 0.09265648152075752,
  0.7961338693570472, 0.16267741639447741, 0.041188714248475373,
  0.7068400808109625, 0.25358901421887947, 0.03957090497015804,
  0.5991550585073127, 0.36225224131779127, 0.038592700174896126,
  0.6238424605572401, 0.28162257770616084, 0.09453496173659899,
  0.6093393403750466, 0.3832726649926592, 0.007387994632294238,
  0.7187036443214267, 0.2737503525162605, 0.007546003162312815,
  0.8986440987448518, 0.09412134279736603, 0.007234558457782137,
  0.724037578585869, 0.18039615188676572, 0.09556626952736523,
  0.8172747318363464, 0.17473734628280568, 0.007987921880847964,
  0.9546336170785, 0.03729147205129122, 0.008074910870208776,
  0.1703672824624436, 0.5881529574639623, 0.241479760073594,
  0.16975979586073597, 0.5012643952150376, 0.3289758089242264,
  0.0383182258210194, 0.8685143643990995, 0.09316740977988115,
  0.09265648152075756, 0.5128232386790481, 0.39452027980019433,
  0.04118871424847537, 0.7961338693570472, 0.16267741639447741,
  0.03957090497015803, 0.7068400808109625, 0.25358901421887947,
  0.03859270017489602, 0.5991550585073127, 0.36225224131779127,
  0.09453496173659903, 0.6238424605572401, 0.28162257770616084,
  0.007387994632294226, 0.6093393403750466, 0.3832726649926592,
  0.007546003162312687, 0.7187036443214267, 0.2737503525162605,
  0.007234558457782092, 0.8986440987448518, 0.09412134279736603,
  0.09556626952736524, 0.724037578585869, 0.18039615188676572,
  0.007987921880847959, 0.8172747318363464, 0.17473734628280568,
  0.008074910870208729, 0.9546336170785, 0.03729147205129122,
  0.24147976007359395, 0.17036728246244368, 0.5881529574639623,
  0.3289758089242264, 0.169759795860736, 0.5012643952150376,
  0.09316740977988114, 0.03831822582101938, 0.8685143643990995,
  0.39452027980019433, 0.09265648152075752, 0.5128232386790481,
  0.16267741639447741, 0.041188714248475373, 0.7961338693570472,
  0.25358901421887947, 0.03957090497015804, 0.7068400808109625,
  0.3622522413177912, 0.038592700174896126, 0.5991550585073127,
  0.28162257770616084, 0.09453496173659899, 0.6238424605572401,
  0.3832726649926592, 0.007387994632294238, 0.6093393403750466,
  0.27375035251626045, 0.007546003162312815, 0.7187036443214267,
  0.09412134279736606, 0.007234558457782137, 0.8986440987448518,
  0.18039615188676572, 0.09556626952736523, 0.724037578585869,
  0.17473734628280568, 0.007987921880847964, 0.8172747318363464,
  0.03729147205129124, 0.008074910870208776, 0.9546336170785,
};
const double triangleRule24Weights[] = {
  0.01254568984560032,
  0.013110532701885239,
  0.010379016056400193,
  0.0038336997309291834,
  0.0006172545054966432,
  0.004343246722170698,
  0.020520008671509844,
  0.010352494770852603,
  0.010027393067388906,
  0.018994586517352658,
  0.013110532701885239,
  0.010379016056400193,
  0.0038336997309291834,
  0.0006172545054966432,
  0.004343246722170698,
  0.020520008671509844,
  0.010352494770852603,
  0.010027393067388906,
  0.018994586517352658,
  0.013110532701885239,
  0.010379016056400193,
  0.0038336997309291834,
  0.0006172545054966432,
  0.004343246722170698,
  0.020520008671509844,
  0.010352494770852603,
  0.010027393067388906,
  0.018994586517352658,
  0.014145045806484846,
  0.015274442601324626,
  0.005366271454167768,
  0.015031854349741339,
  0.0072041341747974275,
  0.008904876928163564,
  0.009947251875682418,
  0.014352351578157454,
  0.004242149266803769,
  0.004081275077116451,
  0.002589212382397985,
  0.01184356214254311,
  0.0037072267642463083,
  0.0017969475854465765,
  0.014145045806484846,
  0.015274442601324626,
  0.005366271454167768,
  0.015031854349741339,
  0.0072041341747974275,
  0.008904876928163564,
  0.009947251875682418,
  0.014352351578157454,
  0.004242149266803769,
  0.004081275077116451,
  0.002589212382397985,
  0.01184356214254311,
  0.0037072267642463083,
  0.0017969475854465765,
  0.014145045806484846,
  0.015274442601324626,
  0.005366271454167768,
  0.015031854349741339,
  0.0072041341747974275,
  0.008904876928163564,
  0.009947251875682418,
  0.014352351578157454,
  0.004242149266803769,
  0.004081275077116451,
  0.002589212382397985,
  0.01184356214254311,
  0.0037072267642463083,
  0.0017969475854465765,
  0.014145045806484846,
  0.015274442601324626,
  0.005366271454167768,
  0.015031854349741339,
  0.0072041341747974275,
  0.008904876928163564,
  0.009947251875682418,
  0.014352351578157454,
  0.004242149266803769,
  0.004081275077116451,
  0.002589212382397985,
  0.01184356214254311,
  0.0037072267642463083,
  0.0017969475854465765,
  0.014145045806484846,
  0.015274442601324626,
  0.005366271454167768,
  0.015031854349741339,
  0.0072041341747974275,
  0.008904876928163564,
  0.009947251875682418,
  0.014352351578157454,
  0.004242149266803769,
  0.004081275077116451,
  0.002589212382397985,
  0.01184356214254311,
  0.0037072267642463083,
  0.0017969475854465765,
  0.014145045806484846,
  0.015274442601324626,
  0.005366271454167768,
  0.015031854349741339,
  0.0072041341747974275,
  0.008904876928163564,
  0.009947251875682418,
  0.014352351578157454,
  0.004242149266803769,
  0.004081275077116451,
  0.002589212382397985,
  0.01184356214254311,
  0.0037072267642463083,
  0.0017969475854465765,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double triangleRule25Points[] = {
  0.22471593919087318, 0.3876420304045634, 0.3876420304045634,
  0.5779909838770066, 0.21100450806149668, 0.21100450806149668,
  0.40101536839098295, 0.2994923158045085, 0.2994923158045085,
  0.9255541480151183, 0.03722292599244087, 0.03722292599244087,
  0.7097815128509992, 0.1451092435745004, 0.1451092435745004,
  0.1504813909188505, 0.42475930454057476, 0.42475930454057476,
  0.07558258250258776, 0.4622087087487061, 0.4622087087487061,
  0.8141005965984601, 0.09294970170076994, 0.09294970170076994,
  0.9843293114347923, 0.007835344282603851, 0.007835344282603851,
  0.021921260679209076, 0.48903936966039546, 0.48903936966039546,
  0.38764203040456335, 0.3876420304045634, 0.22471593919087318,
  0.21100450806149662, 0.21100450806149668, 0.5779909838770066,
  0.2994923158045085, 0.2994923158045085, 0.40101536839098295,
  0.037222925992440814, 0.03722292599244087, 0.9255541480151183,
  0.1451092435745004, 0.1451092435745004, 0.7097815128509992,
  0.42475930454057476, 0.42475930454057476, 0.1504813909188505,
  0.4622087087487061, 0.4622087087487061, 0.07558258250258776,
  0.09294970170076988, 0.09294970170076994, 0.8141005965984601,
  0.007835344282603796, 0.007835344282603851, 0.9843293114347923,
  0.4890393696603954, 0.48903936966039546, 0.021921260679209076,
  0.38764203040456335, 0.22471593919087318, 0.3876420304045634,
  0.21100450806149662, 0.5779909838770066, 0.21100450806149668,
  0.2994923158045085, 0.40101536839098295, 0.2994923158045085,
  0.037222925992440814, 0.9255541480151183, 0.03722292599244087,
  0.1451092435745004, 0.7097815128509992, 0.1451092435745004,
  0.42475930454057476, 0.1504813909188505, 0.42475930454057476,
  0.4622087087487061, 0.07558258250258776, 0.4622087087487061,
  0.09294970170076988, 0.8141005965984601, 0.09294970170076994,
  0.007835344282603796, 0.9843293114347923, 0.007835344282603851,
  0.4890393696603954, 0.021921260679209076, 0.48903936966039546,
  0.5577642058863823, 0.0018188666342743875, 0.4404169274793433,
  0.8040319522230006, 0.03696014157967147, 0.15900790619732788,
  0.7437881352371118, 0.07885806800563527, 0.1773537967572529,
  0.6610857347475427, 0.06884752943149791, 0.2700667358209594,
  0.5426091593378899, 0.11599980764096017, 0.34139103302114987,
  0.5777445859930386, 0.04831743428737695, 0.3739379797195844,
  0.8937386221570603, 0.007128314501257424, 0.09913306334168219,
  0.4968006707860745, 0.20369291058425096, 0.29950641862967453,
  0.8141339896484356, 0.007236161747948156, 0.17862984860361625,
  0.6250173148539955, 0.012913883250032529, 0.362068801895972,
  0.8735191347263744, 0.037687949784259066, 0.08879291548936656,
  0.6293704957712138, 0.13700669408707095, 0.23362281014171524,
  0.7188645300434559, 0.02454006024752439, 0.2565954097090198,
  0.9517423526265223, 0.007188828261693038, 0.041068819111784644,
  0.7196923470332411, 0.0008914643174981278, 0.2794161886492607,
  0.44041692747934325, 0.5577642058863823, 0.0018188666342743875,
  0.15900790619732785, 0.8040319522230007, 0.03696014157967147,
  0.17735379675725294, 0.7437881352371118, 0.07885806800563527,
  0.2700667358209594, 0.6610857347475427, 0.06884752943149791,
  0.3413910330211499, 0.5426091593378899, 0.11599980764096017,
  0.3739379797195843, 0.5777445859930387, 0.04831743428737695,
  0.09913306334168215, 0.8937386221570605, 0.007128314501257424,
  0.29950641862967453, 0.4968006707860745, 0.20369291058425096,
  0.1786298486036162, 0.8141339896484356, 0.007236161747948156,
  0.362068801895972, 0.6250173148539955, 0.012913883250032529,
  0.08879291548936652, 0.8735191347263744, 0.037687949784259066,
  0.23362281014171526, 0.6293704957712138, 0.13700669408707095,
  0.25659540970901984, 0.7188645300434557, 0.02454006024752439,
  0.041068819111784616, 0.9517423526265223, 0.007188828261693038,
  0.27941618864926066, 0.7196923470332413, 0.0008914643174981278,
  0.0018188666342744408, 0.4404169274793433, 0.5577642058863823,
  0.036960141579671424, 0.15900790619732788, 0.8040319522230007,
  0.07885806800563522, 0.1773537967572529, 0.7437881352371118,
  0.06884752943149786, 0.2700667358209594, 0.6610857347475427,
  0.1159998076409603, 0.34139103302114987, 0.5426091593378899,
  0.04831743428737689, 0.3739379797195844, 0.5777445859930387,
  0.007128314501257393, 0.09913306334168219, 0.8937386221570605,
  0.20369291058425099, 0.29950641862967453, 0.4968006707860745,
  0.007236161747948167, 0.17862984860361625, 0.8141339896484356,
  0.01291388325003251, 0.362068801895972, 0.6250173148539955,
  0.037687949784259045, 0.08879291548936656, 0.8735191347263744,
  0.1370066940870709, 0.23362281014171524, 0.6293704957712138,
  0.02454006024752453, 0.2565954097090198, 0.7188645300434557,
  0.007188828261693092, 0.041068819111784644, 0.9517423526265223,
  0.0008914643174979808, 0.2794161886492607, 0.7196923470332413,
  0.5577642058863823, 0.4404169274793433, 0.0018188666342743875,
  0.8040319522230006, 0.15900790619732788, 0.03696014157967147,
  0.7437881352371118, 0.1773537967572529, 0.07885806800563527,
  0.6610857347475427, 0.2700667358209594, 0.06884752943149791,
  0.5426091593378899, 0.34139103302114987, 0.11599980764096017,
  0.5777445859930386, 0.3739379797195844, 0.04831743428737695,
  0.8937386221570603, 0.09913306334168219, 0.007128314501257424,
  0.4968006707860745, 0.29950641862967453, 0.20369291058425096,
  0.8141339896484356, 0.17862984860361625, 0.007236161747948156,
  0.6250173148539955, 0.362068801895972, 0.012913883250032529,
  0.8735191347263744, 0.08879291548936656, 0.037687949784259066,
  0.6293704957712138, 0.23362281014171524, 0.13700669408707095,
  0.7188645300434559, 0.2565954097090198, 0.02454006024752439,
  0.9517423526265223, 0.041068819111784644, 0.007188828261693038,
  0.7196923470332411, 0.2794161886492607, 0.0008914643174981278,
  0.0018188666342744408, 0.5577642058863823, 0.4404169274793433,
  0.036960141579671424, 0.8040319522230007, 0.15900790619732788,
  0.07885806800563522, 0.7437881352371118, 0.1773537967572529,
  0.06884752943149786, 0.6610857347475427, 0.2700667358209594,
  0.1159998076409603, 0.5426091593378899, 0.34139103302114987,
  0.04831743428737689, 0.5777445859930387, 0.3739379797195844,
  0.007128314501257393, 0.8937386221570605, 0.09913306334168219,
  0.20369291058425099, 0.4968006707860745, 0.29950641862967453,
  0.007236161747948167, 0.8141339896484356, 0.17862984860361625,
  0.01291388325003251, 0.6250173148539955, 0.362068801895972,
  0.037687949784259045, 0.8735191347263744, 0.08879291548936656,
  0.1370066940870709, 0.6293704957712138, 0.23362281014171524,
  0.02454006024752453, 0.7188645300434557, 0.2565954097090198,
  0.007188828261693092, 0.9517423526265223, 0.041068819111784644,
  0.0008914643174979808, 0.7196923470332413, 0.2794161886492607,
  0.44041692747934325, 0.0018188666342743875, 0.5577642058863823,
  0.15900790619732785, 0.03696014157967147, 0.8040319522230007,
  0.17735379675725294, 0.07885806800563527, 0.7437881352371118,
  0.2700667358209594, 0.06884752943149791, 0.6610857347475427,
  0.3413910330211499, 0.11599980764096017, 0.5426091593378899,
  0.3739379797195843, 0.04831743428737695, 0.5777445859930387,
  0.09913306334168215, 0.007128314501257424, 0.8937386221570605,
  0.29950641862967453, 0.20369291058425096, 0.4968006707860745,
  0.1786298486036162, 0.007236161747948156, 0.8141339896484356,
  0.362068801895972, 0.012913883250032529, 0.6250173148539955,
  0.08879291548936652, 0.037687949784259066, 0.8735191347263744,
  0.23362281014171526, 0.13700669408707095, 0.6293704957712138,
  0.25659540970901984, 0.02454006024752439, 0.7188645300434557,
  0.041068819111784616, 0.007188828261693038, 0.9517423526265223,
  0.27941618864926066, 0.0008914643174981278, 0.7196923470332413,
};
const double triangleRule25Weights[] = {
  0.013689851548272245,
  0.011587263236010593,
  0.018017640701701476,
  0.003397297721904736,
  0.011491525862564798,
  0.01591131013745842,
  0.013654275187528014,
  0.009182821259820036,
  0.0008065102883246168,
  0.008444085946521077,
  0.013689851548272245,
  0.011587263236010593,
  0.018017640701701476,
  0.003397297721904736,
  0.011491525862564798,
  0.01591131013745842,
  0.013654275187528014,
  0.009182821259820036,
  0.0008065102883246168,
  0.008444085946521077,
  0.013689851548272245,
  0.011587263236010593,
  0.018017640701701476,
  0.003397297721904736,
  0.011491525862564798,
  0.01591131013745842,
  0.013654275187528014,
  0.009182821259820036,
  0.0008065102883246168,
  0.008444085946521077,
  0.0016748178319347053,
  0.006311478024759274,
  0.009515021567455772,
  0.01088439361243692,
  0.015840352287898436,
  0.010640170695508785,
  0.0025452716253490143,
  0.01791382089227606,
  0.003263739682049243,
  0.005454638367974429,
  0.00527256192142942,
  0.013740082592022551,
  0.007314340907932847,
  0.0016929836341273324,
  0.0015117020784588804,
  0.0016748178319347053,
  0.006311478024759274,
  0.009515021567455772,
  0.01088439361243692,
  0.015840352287898436,
  0.010640170695508785,
  0.0025452716253490143,
  0.01791382089227606,
  0.003263739682049243,
  0.005454638367974429,
  0.00527256192142942,
  0.013740082592022551,
  0.007314340907932847,
  0.0016929836341273324,
  0.0015117020784588804,
  0.0016748178319347053,
  0.006311478024759274,
  0.009515021567455772,
  0.01088439361243692,
  0.015840352287898436,
  0.010640170695508785,
  0.0025452716253490143,
  0.01791382089227606,
  0.003263739682049243,
  0.005454638367974429,
  0.00527256192142942,
  0.013740082592022551,
  0.007314340907932847,
  0.0016929836341273324,
  0.0015117020784588804,
  0.0016748178319347053,
  0.006311478024759274,
  0.009515021567455772,
  0.01088439361243692,
  0.015840352287898436,
  0.010640170695508785,
  0.0025452716253490143,
  0.01791382089227606,
  0.003263739682049243,
  0.005454638367974429,
  0.00527256192142942,
  0.013740082592022551,
  0.007314340907932847,
  0.0016929836341273324,
  0.0015117020784588804,
  0.0016748178319347053,
  0.006311478024759274,
  0.009515021567455772,
  0.01088439361243692,
  0.015840352287898436,
  0.010640170695508785,
  0.0025452716253490143,
  0.01791382089227606,
  0.003263739682049243,
  0.005454638367974429,
  0.00527256192142942,
  0.013740082592022551,
  0.007314340907932847,
  0.0016929836341273324,
  0.0015117020784588804,
  0.0016748178319347053,
  0.006311478024759274,
  0.009515021567455772,
  0.01088439361243692,
  0.015840352287898436,
  0.010640170695508785,
  0.0025452716253490143,
  0.01791382089227606,
  0.003263739682049243,
  0.005454638367974429,
  0.00527256192142942,
  0.013740082592022551,
  0.007314340907932847,
  0.0016929836341273324,
  0.0015117020784588804,
};
const double triangleRule26Points[] = {
  0.33333333333333337, 0.3333333333333333, 0.3333333333333333,
  0.8665257548470675, 0.06673712257646625, 0.06673712257646625,
  0.9873197670158461, 0.0063401164920769415, 0.0063401164920769415,
  0.01249393420723044, 0.4937530328963848, 0.4937530328963848,
  0.22242500578481195, 0.388787497107594, 0.388787497107594,
  0.4537057981418424, 0.2731471009290788, 0.2731471009290788,
  0.056342873357667966, 0.471828563321166, 0.471828563321166,
  0.6915971392709114, 0.1542014303645443, 0.1542014303645443,
  0.5759136733955886, 0.21204316330220568, 0.21204316330220568,
  0.12802916123123365, 0.4359854193843832, 0.4359854193843832,
  0.06673712257646625, 0.06673712257646625, 0.8665257548470675,
  0.006340116492076886, 0.0063401164920769415, 0.9873197670158461,
  0.49375303289638484, 0.4937530328963848, 0.01249393420723044,
  0.38878749710759397, 0.388787497107594, 0.22242500578481195,
  0.2731471009290788, 0.2731471009290788, 0.4537057981418424,
  0.4718285633211661, 0.471828563321166, 0.056342873357667966,
  0.15420143036454426, 0.1542014303645443, 0.6915971392709114,
  0.21204316330220574, 0.21204316330220568, 0.5759136733955886,
  0.4359854193843832, 0.4359854193843832, 0.12802916123123365,
  0.06673712257646625, 0.8665257548470675, 0.06673712257646625,
  0.006340116492076886, 0.9873197670158461, 0.0063401164920769415,
  0.49375303289638484, 0.01249393420723044, 0.4937530328963848,
  0.38878749710759397, 0.22242500578481195, 0.388787497107594,
  0.2731471009290788, 0.4537057981418424, 0.2731471009290788,
  0.4718285633211661, 0.056342873357667966, 0.471828563321166,
  0.15420143036454426, 0.6915971392709114, 0.1542014303645443,
  0.21204316330220574, 0.5759136733955886, 0.21204316330220568,
  0.4359854193843832, 0.12802916123123365, 0.4359854193843832,
  0.9151336840842468, 0.004794660975436677, 0.08007165494031654,
  0.9392011922216333, 0.029155196206835834, 0.031643611571530776,
  0.8984105884621026, 0.02620936402249865, 0.07538004751539866,
  0.9612018477470925, 0.005698117916875216, 0.03310003433603227,
  0.8257890876433118, 0.041724722742120926, 0.13248618961456732,
  0.7912672079790704, 0.10004565910652752, 0.10868713291440213,
  0.6291132845042245, 0.120614402205249, 0.25027231329052646,
  0.5814399954403304, 0.029537942516907823, 0.3890220620427618,
  0.554112238408494, 0.08737846516384448, 0.35850929642766155,
  0.7368189190108191, 0.07631190151295938, 0.18686917947622156,
  0.5832365594443228, 0.002057530965370865, 0.4147059095903063,
  0.5101059661193124, 0.1704787284972489, 0.31941530538343876,
  0.8482627657087517, 0.007999608091484301, 0.14373762619976402,
  0.6650459874553918, 0.05116587368513777, 0.2837881388594704,
  0.7606687342756272, 0.02278459925089566, 0.21654666647347712,
  0.6776281990129065, 0.009473297912213558, 0.31289850307488,
  0.7731011948601069, 0.0004640077321756526, 0.22643479740771752,
  0.08007165494031654, 0.9151336840842468, 0.004794660975436677,
  0.03164361157153073, 0.9392011922216335, 0.029155196206835834,
  0.07538004751539862, 0.8984105884621028, 0.02620936402249865,
  0.03310003433603226, 0.9612018477470925, 0.005698117916875216,
  0.13248618961456726, 0.8257890876433118, 0.041724722742120926,
  0.10868713291440213, 0.7912672079790704, 0.10004565910652752,
  0.25027231329052646, 0.6291132845042245, 0.120614402205249,
  0.3890220620427618, 0.5814399954403304, 0.029537942516907823,
  0.3585092964276615, 0.554112238408494, 0.08737846516384448,
  0.18686917947622161, 0.736818919010819, 0.07631190151295938,
  0.4147059095903063, 0.5832365594443228, 0.002057530965370865,
  0.31941530538343876, 0.5101059661193124, 0.1704787284972489,
  0.14373762619976405, 0.8482627657087517, 0.007999608091484301,
  0.2837881388594704, 0.6650459874553918, 0.05116587368513777,
  0.2165466664734771, 0.7606687342756272, 0.02278459925089566,
  0.31289850307488, 0.6776281990129065, 0.009473297912213558,
  0.22643479740771755, 0.7731011948601068, 0.0004640077321756526,
  0.004794660975436682, 0.08007165494031654, 0.9151336840842468,
  0.02915519620683582, 0.031643611571530776, 0.9392011922216335,
  0.026209364022498627, 0.07538004751539866, 0.8984105884621028,
  0.005698117916875245, 0.03310003433603227, 0.9612018477470925,
  0.04172472274212091, 0.13248618961456732, 0.8257890876433118,
  0.10004565910652752, 0.10868713291440213, 0.7912672079790704,
  0.120614402205249, 0.25027231329052646, 0.6291132845042245,
  0.029537942516907778, 0.3890220620427618, 0.5814399954403304,
  0.08737846516384451, 0.35850929642766155, 0.554112238408494,
  0.07631190151295941, 0.18686917947622156, 0.736818919010819,
  0.0020575309653708684, 0.4147059095903063, 0.5832365594443228,
  0.17047872849724888, 0.31941530538343876, 0.5101059661193124,
  0.007999608091484256, 0.14373762619976402, 0.8482627657087517,
  0.05116587368513781, 0.2837881388594704, 0.6650459874553918,
  0.02278459925089571, 0.21654666647347712, 0.7606687342756272,
  0.009473297912213519, 0.31289850307488, 0.6776281990129065,
  0.00046400773217569746, 0.22643479740771752, 0.7731011948601068,
  0.9151336840842468, 0.08007165494031654, 0.004794660975436677,
  0.9392011922216333, 0.031643611571530776, 0.029155196206835834,
  0.8984105884621026, 0.07538004751539866, 0.02620936402249865,
  0.9612018477470925, 0.03310003433603227, 0.005698117916875216,
  0.8257890876433118, 0.13248618961456732, 0.041724722742120926,
  0.7912672079790704, 0.10868713291440213, 0.10004565910652752,
  0.6291132845042245, 0.25027231329052646, 0.120614402205249,
  0.5814399954403304, 0.3890220620427618, 0.029537942516907823,
  0.554112238408494, 0.35850929642766155, 0.08737846516384448,
  0.7368189190108191, 0.18686917947622156, 0.07631190151295938,
  0.5832365594443228, 0.4147059095903063, 0.002057530965370865,
  0.5101059661193124, 0.31941530538343876, 0.1704787284972489,
  0.8482627657087517, 0.14373762619976402, 0.007999608091484301,
  0.6650459874553918, 0.2837881388594704, 0.05116587368513777,
  0.7606687342756272, 0.21654666647347712, 0.02278459925089566,
  0.6776281990129065, 0.31289850307488, 0.009473297912213558,
  0.7731011948601069, 0.22643479740771752, 0.0004640077321756526,
  0.004794660975436682, 0.9151336840842468, 0.08007165494031654,
  0.02915519620683582, 0.9392011922216335, 0.031643611571530776,
  0.026209364022498627, 0.8984105884621028, 0.07538004751539866,
  0.005698117916875245, 0.9612018477470925, 0.03310003433603227,
  0.04172472274212091, 0.8257890876433118, 0.13248618961456732,
  0.10004565910652752, 0.7912672079790704, 0.10868713291440213,
  0.120614402205249, 0.6291132845042245, 0.25027231329052646,
  0.029537942516907778, 0.5814399954403304, 0.3890220620427618,
  0.08737846516384451, 0.554112238408494, 0.35850929642766155,
  0.07631190151295941, 0.736818919010819, 0.18686917947622156,
  0.0020575309653708684, 0.5832365594443228, 0.4147059095903063,
  0.17047872849724888, 0.5101059661193124, 0.31941530538343876,
  0.007999608091484256, 0.8482627657087517, 0.14373762619976402,
  0.05116587368513781, 0.6650459874553918, 0.2837881388594704,
  0.02278459925089571, 0.7606687342756272, 0.21654666647347712,
  0.009473297912213519, 0.6776281990129065, 0.31289850307488,
  0.00046400773217569746, 0.7731011948601068, 0.22643479740771752,
  0.08007165494031654, 0.004794660975436677, 0.9151336840842468,
  0.03164361157153073, 0.029155196206835834, 0.9392011922216335,
  0.07538004751539862, 0.02620936402249865, 0.8984105884621028,
  0.03310003433603226, 0.005698117916875216, 0.9612018477470925,
  0.13248618961456726, 0.041724722742120926, 0.8257890876433118,
  0.10868713291440213, 0.10004565910652752, 0.7912672079790704,
  0.25027231329052646, 0.120614402205249, 0.6291132845042245,
  0.3890220620427618, 0.029537942516907823, 0.5814399954403304,
  0.3585092964276615, 0.08737846516384448, 0.554112238408494,
  0.18686917947622161, 0.07631190151295938, 0.736818919010819,
  0.4147059095903063, 0.002057530965370865, 0.5832365594443228,
  0.31941530538343876, 0.1704787284972489, 0.5101059661193124,
  0.14373762619976405, 0.007999608091484301, 0.8482627657087517,
  0.2837881388594704, 0.05116587368513777, 0.6650459874553918,
  0.2165466664734771, 0.02278459925089566, 0.7606687342756272,
  0.31289850307488, 0.009473297912213558, 0.6776281990129065,
  0.22643479740771755, 0.0004640077321756526, 0.7731011948601068,
};
const double triangleRule26Weights[] = {
  0.020486662589223242,
  0.004913825302966018,
  0.0005269531166818719,
  0.005302159181867346,
  0.01946806783718288,
  0.01953564692324754,
  0.011528503634656892,
  0.013255259448545269,
  0.01694434507852809,
  0.016412400602587904,
  0.004913825302966018,
  0.0005269531166818719,
  0.005302159181867346,
  0.01946806783718288,
  0.01953564692324754,
  0.011528503634656892,
  0.013255259448545269,
  0.01694434507852809,
  0.016412400602587904,
  0.004913825302966018,
  0.0005269531166818719,
  0.005302159181867346,
  0.01946806783718288,
  0.01953564692324754,
  0.011528503634656892,
  0.013255259448545269,
  0.01694434507852809,
  0.016412400602587904,
  0.0013985264481602723,
  0.0012055647737168856,
  0.0033055447129676702,
  0.001085707342996755,
  0.006403597899712819,
  0.004614211076378318,
  0.01437947322759874,
  0.00825976721708684,
  0.013727958216085703,
  0.010397645528174324,
  0.001857147470998084,
  0.01759916718069521,
  0.0029667616626565057,
  0.010107124432088685,
  0.006269337846080569,
  0.004591558387398637,
  0.0011395489158682135,
  0.0013985264481602723,
  0.0012055647737168856,
  0.0033055447129676702,
  0.001085707342996755,
  0.006403597899712819,
  0.004614211076378318,
  0.01437947322759874,
  0.00825976721708684,
  0.013727958216085703,
  0.010397645528174324,
  0.001857147470998084,
  0.01759916718069521,
  0.0029667616626565057,
  0.010107124432088685,
  0.006269337846080569,
  0.004591558387398637,
  0.0011395489158682135,
  0.0013985264481602723,
  0.0012055647737168856,
  0.0033055447129676702,
  0.001085707342996755,
  0.006403597899712819,
  0.004614211076378318,
  0.01437947322759874,
  0.00825976721708684,
  0.013727958216085703,
  0.010397645528174324,
  0.001857147470998084,
  0.01759916718069521,
  0.0029667616626565057,
  0.010107124432088685,
  0.006269337846080569,
  0.004591558387398637,
  0.0011395489158682135,
  0.0013985264481602723,
  0.0012055647737168856,
  0.0033055447129676702,
  0.001085707342996755,
  0.006403597899712819,
  0.004614211076378318,
  0.01437947322759874,
  0.00825976721708684,
  0.013727958216085703,
  0.010397645528174324,
  0.001857147470998084,
  0.01759916718069521,
  0.0029667616626565057,
  0.010107124432088685,
  0.006269337846080569,
  0.004591558387398637,
  0.0011395489158682135,
  0.0013985264481602723,
  0.0012055647737168856,
  0.0033055447129676702,
  0.001085707342996755,
  0.006403597899712819,
  0.004614211076378318,
  0.01437947322759874,
  0.00825976721708684,
  0.013727958216085703,
  0.010397645528174324,
  0.001857147470998084,
  0.01759916718069521,
  0.0029667616626565057,
  0.010107124432088685,
  0.006269337846080569,
  0.004591558387398637,
  0.0011395489158682135,
  0.0013985264481602723,
  0.0012055647737168856,
  0.0033055447129676702,
  0.001085707342996755,
  0.006403597899712819,
  0.004614211076378318,
  0.01437947322759874,
  0.00825976721708684,
  0.013727958216085703,
  0.010397645528174324,
  0.001857147470998084,
  0.01759916718069521,
  0.0029667616626565057,
  0.010107124432088685,
  0.006269337846080569,
  0.004591558387398637,
  0.0011395489158682135,
};
const double triangleRule27Points[] = {
  0.23857195763762562, 0.3807140211811872, 0.3807140211811872,
  0.10666439259227078, 0.4466678037038646, 0.4466678037038646,
  0.16771724238917574, 0.41614137880541213, 0.41614137880541213,
  0.8393907044231231, 0.08030464778843843, 0.08030464778843843,
  0.5331991866602577, 0.23340040666987116, 0.23340040666987116,
  0.39766906966698157, 0.3011654651665092, 0.3011654651665092,
  0.6504400672901999, 0.17477996635490006, 0.17477996635490006,
  0.02886989162967446, 0.48556505418516277, 0.48556505418516277,
  0.9348569596396366, 0.03257152018018172, 0.03257152018018172,
  0.7448581961906448, 0.12757090190467762, 0.12757090190467762,
  0.9867215616380822, 0.0066392191809588885, 0.0066392191809588885,
  0.38071402118118725, 0.3807140211811872, 0.23857195763762562,
  0.4466678037038646, 0.4466678037038646, 0.10666439259227078,
  0.41614137880541213, 0.41614137880541213, 0.16771724238917574,
  0.08030464778843838, 0.08030464778843843, 0.8393907044231231,
  0.23340040666987116, 0.23340040666987116, 0.5331991866602577,
  0.3011654651665092, 0.3011654651665092, 0.39766906966698157,
  0.17477996635490012, 0.17477996635490006, 0.6504400672901999,
  0.4855650541851628, 0.48556505418516277, 0.02886989162967446,
  0.03257152018018172, 0.03257152018018172, 0.9348569596396366,
  0.12757090190467757, 0.12757090190467762, 0.7448581961906448,
  0.0066392191809588885, 0.0066392191809588885, 0.9867215616380822,
  0.38071402118118725, 0.23857195763762562, 0.3807140211811872,
  0.4466678037038646, 0.10666439259227078, 0.4466678037038646,
  0.41614137880541213, 0.16771724238917574, 0.41614137880541213,
  0.08030464778843838, 0.8393907044231231, 0.08030464778843843,
  0.23340040666987116, 0.5331991866602577, 0.23340040666987116,
  0.3011654651665092, 0.39766906966698157, 0.3011654651665092,
  0.17477996635490012, 0.6504400672901999, 0.17477996635490006,
  0.4855650541851628, 0.02886989162967446, 0.48556505418516277,
  0.03257152018018172, 0.9348569596396366, 0.03257152018018172,
  0.12757090190467757, 0.7448581961906448, 0.12757090190467762,
  0.0066392191809588885, 0.9867215616380822, 0.0066392191809588885,
  0.6822271986792305, 0.030730604727272855, 0.2870421965934966,
  0.525759518220982, 0.12915264006344968, 0.3450878417155684,
  0.5960363568560882, 0.028033486095250002, 0.3759301570486618,
  0.4739234899291993, 0.20913092113766868, 0.31694558893313196,
  0.5267326941075414, 0.06603891284973865, 0.4072283930427199,
  0.7454158247229943, 0.041030576819181826, 0.21355359845782393,
  0.6658474815593083, 0.005299640371799034, 0.32885287806889263,
  0.7976306984429004, 0.06307399541495087, 0.13929530614214874,
  0.5957908943647818, 0.1489628509382401, 0.25524625469697804,
  0.6969269019664952, 0.09469708243313069, 0.20837601560037405,
  0.5544087310385244, 0.005580717015260116, 0.44001055194621547,
  0.6227021563389827, 0.07507690243319622, 0.3022209412278211,
  0.9110706680920073, 0.0069825293244590156, 0.08194680258353369,
  0.9595414606840932, 0.0060935694037648315, 0.03436496991214199,
  0.8848535036252015, 0.03503442252769738, 0.08011207384710112,
  0.8334345667830385, 0.019352001318038967, 0.14721343189892247,
  0.7629478741931164, 0.007332472549040455, 0.22971965325784321,
  0.8518541504366672, 0.0004903284434629743, 0.1476555211198698,
  0.2870421965934966, 0.6822271986792305, 0.030730604727272855,
  0.3450878417155685, 0.5257595182209819, 0.12915264006344968,
  0.37593015704866173, 0.5960363568560882, 0.028033486095250002,
  0.31694558893313185, 0.4739234899291994, 0.20913092113766868,
  0.40722839304271996, 0.5267326941075414, 0.06603891284973865,
  0.21355359845782396, 0.7454158247229942, 0.041030576819181826,
  0.32885287806889263, 0.6658474815593083, 0.005299640371799034,
  0.1392953061421487, 0.7976306984429005, 0.06307399541495087,
  0.25524625469697804, 0.5957908943647818, 0.1489628509382401,
  0.2083760156003741, 0.6969269019664952, 0.09469708243313069,
  0.4400105519462155, 0.5544087310385244, 0.005580717015260116,
  0.30222094122782106, 0.6227021563389827, 0.07507690243319622,
  0.0819468025835337, 0.9110706680920073, 0.0069825293244590156,
  0.034364969912141996, 0.9595414606840932, 0.0060935694037648315,
  0.08011207384710117, 0.8848535036252014, 0.03503442252769738,
  0.14721343189892244, 0.8334345667830386, 0.019352001318038967,
  0.22971965325784316, 0.7629478741931164, 0.007332472549040455,
  0.1476555211198698, 0.8518541504366672, 0.0004903284434629743,
  0.030730604727272848, 0.2870421965934966, 0.6822271986792305,
  0.12915264006344973, 0.3450878417155684, 0.5257595182209819,
  0.028033486095250026, 0.3759301570486618, 0.5960363568560882,
  0.20913092113766862, 0.31694558893313196, 0.4739234899291994,
  0.06603891284973873, 0.4072283930427199, 0.5267326941075414,
  0.041030576819181874, 0.21355359845782393, 0.7454158247229942,
  0.005299640371799086, 0.32885287806889263, 0.6658474815593083,
  0.06307399541495085, 0.13929530614214874, 0.7976306984429005,
  0.14896285093824013, 0.25524625469697804, 0.5957908943647818,
  0.0946970824331308, 0.20837601560037405, 0.6969269019664952,
  0.005580717015260195, 0.44001055194621547, 0.5544087310385244,
  0.07507690243319609, 0.3022209412278211, 0.6227021563389827,
  0.006982529324458975, 0.08194680258353369, 0.9110706680920073,
  0.00609356940376482, 0.03436496991214199, 0.9595414606840932,
  0.035034422527697506, 0.08011207384710112, 0.8848535036252014,
  0.019352001318038936, 0.14721343189892247, 0.8334345667830386,
  0.0073324725490404585, 0.22971965325784321, 0.7629478741931164,
  0.0004903284434629729, 0.1476555211198698, 0.8518541504366672,
  0.6822271986792305, 0.2870421965934966, 0.030730604727272855,
  0.525759518220982, 0.3450878417155684, 0.12915264006344968,
  0.5960363568560882, 0.3759301570486618, 0.028033486095250002,
  0.4739234899291993, 0.31694558893313196, 0.20913092113766868,
  0.5267326941075414, 0.4072283930427199, 0.06603891284973865,
  0.7454158247229943, 0.21355359845782393, 0.041030576819181826,
  0.6658474815593083, 0.32885287806889263, 0.005299640371799034,
  0.7976306984429004, 0.13929530614214874, 0.06307399541495087,
  0.5957908943647818, 0.25524625469697804, 0.1489628509382401,
  0.6969269019664952, 0.20837601560037405, 0.09469708243313069,
  0.5544087310385244, 0.44001055194621547, 0.005580717015260116,
  0.6227021563389827, 0.3022209412278211, 0.07507690243319622,
  0.9110706680920073, 0.08194680258353369, 0.0069825293244590156,
  0.9595414606840932, 0.03436496991214199, 0.0060935694037648315,
  0.8848535036252015, 0.08011207384710112, 0.03503442252769738,
  0.8334345667830385, 0.14721343189892247, 0.019352001318038967,
  0.7629478741931164, 0.22971965325784321, 0.007332472549040455,
  0.8518541504366672, 0.1476555211198698, 0.0004903284434629743,
  0.030730604727272848, 0.6822271986792305, 0.2870421965934966,
  0.12915264006344973, 0.5257595182209819, 0.3450878417155684,
  0.028033486095250026, 0.5960363568560882, 0.3759301570486618,
  0.20913092113766862, 0.4739234899291994, 0.31694558893313196,
  0.06603891284973873, 0.5267326941075414, 0.4072283930427199,
  0.041030576819181874, 0.7454158247229942, 0.21355359845782393,
  0.005299640371799086, 0.6658474815593083, 0.32885287806889263,
  0.06307399541495085, 0.7976306984429005, 0.13929530614214874,
  0.14896285093824013, 0.5957908943647818, 0.25524625469697804,
  0.0946970824331308, 0.6969269019664952, 0.20837601560037405,
  0.005580717015260195, 0.5544087310385244, 0.44001055194621547,
  0.07507690243319609, 0.6227021563389827, 0.3022209412278211,
  0.006982529324458975, 0.9110706680920073, 0.08194680258353369,
  0.00609356940376482, 0.9595414606840932, 0.03436496991214199,
  0.035034422527697506, 0.8848535036252014, 0.08011207384710112,
  0.019352001318038936, 0.8334345667830386, 0.14721343189892247,
  0.0073324725490404585, 0.7629478741931164, 0.22971965325784321,
  0.0004903284434629729, 0.8518541504366672, 0.1476555211198698,
  0.2870421965934966, 0.030730604727272855, 0.6822271986792305,
  0.3450878417155685, 0.12915264006344968, 0.5257595182209819,
  0.37593015704866173, 0.028033486095250002, 0.5960363568560882,
  0.31694558893313185, 0.20913092113766868, 0.4739234899291994,
  0.40722839304271996, 0.06603891284973865, 0.5267326941075414,
  0.21355359845782396, 0.041030576819181826, 0.7454158247229942,
  0.32885287806889263, 0.005299640371799034, 0.6658474815593083,
  0.1392953061421487, 0.06307399541495087, 0.7976306984429005,
  0.25524625469697804, 0.1489628509382401, 0.5957908943647818,
  0.2083760156003741, 0.09469708243313069, 0.6969269019664952,
  0.4400105519462155, 0.005580717015260116, 0.5544087310385244,
  0.30222094122782106, 0.07507690243319622, 0.6227021563389827,
  0.0819468025835337, 0.0069825293244590156, 0.9110706680920073,
  0.034364969912141996, 0.0060935694037648315, 0.9595414606840932,
  0.08011207384710117, 0.03503442252769738, 0.8848535036252014,
  0.14721343189892244, 0.019352001318038967, 0.8334345667830386,
  0.22971965325784316, 0.007332472549040455, 0.7629478741931164,
  0.1476555211198698, 0.0004903284434629743, 0.8518541504366672,
};
const double triangleRule27Weights[] = {
  0.00956008496745992,
  0.009410159809454225,
  0.012050227024150434,
  0.0052126218728018765,
  0.013471315398049376,
  0.015747965781362654,
  0.01128244254469838,
  0.007117237412874642,
  0.002777339528954181,
  0.009743244922817732,
  0.0005754424056705024,
  0.00956008496745992,
  0.009410159809454225,
  0.012050227024150434,
  0.0052126218728018765,
  0.013471315398049376,
  0.015747965781362654,
  0.01128244254469838,
  0.007117237412874642,
  0.002777339528954181,
  0.009743244922817732,
  0.0005754424056705024,
  0.00956008496745992,
  0.009410159809454225,
  0.012050227024150434,
  0.0052126218728018765,
  0.013471315398049376,
  0.015747965781362654,
  0.01128244254469838,
  0.007117237412874642,
  0.002777339528954181,
  0.009743244922817732,
  0.0005754424056705024,
  0.0055317948337667315,
  0.012557436204036536,
  0.006395152699454403,
  0.01371539323055084,
  0.00986227011898957,
  0.00645537290492969,
  0.0029278263617991025,
  0.007130635310487024,
  0.012347663130861363,
  0.010693700589616264,
  0.003242467597639341,
  0.010930611092913286,
  0.0020151231272897024,
  0.0011967736084731628,
  0.004327158035360713,
  0.00462238711178111,
  0.003394253738807027,
  0.0008466061357638505,
  0.0055317948337667315,
  0.012557436204036536,
  0.006395152699454403,
  0.01371539323055084,
  0.00986227011898957,
  0.00645537290492969,
  0.0029278263617991025,
  0.007130635310487024,
  0.012347663130861363,
  0.010693700589616264,
  0.003242467597639341,
  0.010930611092913286,
  0.0020151231272897024,
  0.0011967736084731628,
  0.004327158035360713,
  0.00462238711178111,
  0.003394253738807027,
  0.0008466061357638505,
  0.0055317948337667315,
  0.012557436204036536,
  0.006395152699454403,
  0.01371539323055084,
  0.00986227011898957,
  0.00645537290492969,
  0.0029278263617991025,
  0.007130635310487024,
  0.012347663130861363,
  0.010693700589616264,
  0.003242467597639341,
  0.010930611092913286,
  0.0020151231272897024,
  0.0011967736084731628,
  0.004327158035360713,
  0.00462238711178111,
  0.003394253738807027,
  0.0008466061357638505,
  0.0055317948337667315,
  0.012557436204036536,
  0.006395152699454403,
  0.01371539323055084,
  0.00986227011898957,
  0.00645537290492969,
  0.0029278263617991025,
  0.007130635310487024,
  0.012347663130861363,
  0.010693700589616264,
  0.003242467597639341,
  0.010930611092913286,
  0.0020151231272897024,
  0.0011967736084731628,
  0.004327158035360713,
  0.00462238711178111,
  0.003394253738807027,
  0.0008466061357638505,
  0.0055317948337667315,
  0.012557436204036536,
  0.006395152699454403,
  0.01371539323055084,
  0.00986227011898957,
  0.00645537290492969,
  0.0029278263617991025,
  0.007130635310487024,
  0.012347663130861363,
  0.010693700589616264,
  0.003242467597639341,
  0.010930611092913286,
  0.0020151231272897024,
  0.0011967736084731628,
  0.004327158035360713,
  0.00462238711178111,
  0.003394253738807027,
  0.0008466061357638505,
  0.0055317948337667315,
  0.012557436204036536,
  0.006395152699454403,
  0.01371539323055084,
  0.00986227011898957,
  0.00645537290492969,
  0.0029278263617991025,
  0.007130635310487024,
  0.012347663130861363,
  0.010693700589616264,
  0.003242467597639341,
  0.010930611092913286,
  0.0020151231272897024,
  0.0011967736084731628,
  0.004327158035360713,
  0.00462238711178111,
  0.003394253738807027,
  0.0008466061357638505,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double triangleRule28Points[] = {
  0.39203415496703165, 0.3039829225164842, 0.3039829225164842,
  0.9903917476066838, 0.004804126196658098, 0.004804126196658098,
  0.08344019151917614, 0.45827990424041193, 0.45827990424041193,
  0.2274640528599159, 0.38626797357004206, 0.38626797357004206,
  0.4834718556990756, 0.2582640721504622, 0.2582640721504622,
  0.7882083116427446, 0.10589584417862768, 0.10589584417862768,
  0.14089559576220134, 0.42955220211889933, 0.42955220211889933,
  0.030317734874821145, 0.4848411325625894, 0.4848411325625894,
  0.6827246222738805, 0.15863768886305973, 0.15863768886305973,
  0.8783216152144824, 0.06083919239275881, 0.06083919239275881,
  0.3039829225164842, 0.3039829225164842, 0.39203415496703165,
  0.004804126196658043, 0.004804126196658098, 0.9903917476066838,
  0.458279904240412, 0.45827990424041193, 0.08344019151917614,
  0.38626797357004206, 0.38626797357004206, 0.2274640528599159,
  0.2582640721504622, 0.2582640721504622, 0.4834718556990756,
  0.10589584417862774, 0.10589584417862768, 0.7882083116427446,
  0.42955220211889933, 0.42955220211889933, 0.14089559576220134,
  0.4848411325625894, 0.4848411325625894, 0.030317734874821145,
  0.15863768886305973, 0.15863768886305973, 0.6827246222738805,
  0.06083919239275881, 0.06083919239275881, 0.8783216152144824,
  0.3039829225164842, 0.39203415496703165, 0.3039829225164842,
  0.004804126196658043, 0.9903917476066838, 0.004804126196658098,
  0.458279904240412, 0.08344019151917614, 0.45827990424041193,
  0.38626797357004206, 0.2274640528599159, 0.38626797357004206,
  0.2582640721504622, 0.4834718556990756, 0.2582640721504622,
  0.10589584417862774, 0.7882083116427446, 0.10589584417862768,
  0.42955220211889933, 0.14089559576220134, 0.42955220211889933,
  0.4848411325625894, 0.030317734874821145, 0.4848411325625894,
  0.15863768886305973, 0.6827246222738805, 0.15863768886305973,
  0.06083919239275881, 0.8783216152144824, 0.06083919239275881,
  0.9329702140721975, 0.02152438536945612, 0.0455054005583464,
  0.7375358758753532, 0.04906966935755949, 0.2133944547670873,
  0.5802390377843101, 0.17765845029637026, 0.24210251191931964,
  0.4829969116880932, 0.1898123562927368, 0.32719073201917004,
  0.8535434510435365, 0.0044583820232893204, 0.14199816693317424,
  0.7369256303241862, 0.08767797648435202, 0.17539639319146172,
  0.5446800590311748, 0.06318032763441064, 0.39213961333441455,
  0.661704920830155, 0.004149464133923672, 0.33414561503592133,
  0.8030589990229016, 0.022794804925916238, 0.17414619605118214,
  0.7014601475563789, 0.022700844371797004, 0.2758390080718242,
  0.9676276842926838, 0.006149648542663968, 0.026222667164652273,
  0.644919168291803, 0.11203362934227094, 0.24304720236592617,
  0.7652255261691057, 0.004781489772987132, 0.22999298405790716,
  0.6419429769479654, 0.062448742179632866, 0.29560828087240165,
  0.8283953633324808, 0.050211185913428096, 0.12139345075409119,
  0.6004482009469116, 0.025727998742878733, 0.3738238003102097,
  0.5515700274862902, 0.005646565993466159, 0.44278340652024356,
  0.5441122670843226, 0.11808906971509502, 0.3377986632005823,
  0.8895285197924231, 0.018242291012294715, 0.09222918919528221,
  0.9285090039203802, 0.0012002556014871519, 0.07029074047813273,
  0.0455054005583464, 0.9329702140721975, 0.02152438536945612,
  0.2133944547670873, 0.7375358758753532, 0.04906966935755949,
  0.24210251191931964, 0.5802390377843101, 0.17765845029637026,
  0.32719073201917004, 0.4829969116880932, 0.1898123562927368,
  0.14199816693317424, 0.8535434510435365, 0.0044583820232893204,
  0.17539639319146172, 0.7369256303241862, 0.08767797648435202,
  0.3921396133344145, 0.5446800590311749, 0.06318032763441064,
  0.33414561503592133, 0.661704920830155, 0.004149464133923672,
  0.1741461960511822, 0.8030589990229016, 0.022794804925916238,
  0.27583900807182415, 0.7014601475563789, 0.022700844371797004,
  0.02622266716465227, 0.9676276842926838, 0.006149648542663968,
  0.24304720236592614, 0.644919168291803, 0.11203362934227094,
  0.22999298405790713, 0.7652255261691058, 0.004781489772987132,
  0.29560828087240165, 0.6419429769479654, 0.062448742179632866,
  0.12139345075409114, 0.8283953633324808, 0.050211185913428096,
  0.3738238003102097, 0.6004482009469116, 0.025727998742878733,
  0.4427834065202436, 0.5515700274862902, 0.005646565993466159,
  0.3377986632005824, 0.5441122670843226, 0.11808906971509502,
  0.09222918919528222, 0.8895285197924231, 0.018242291012294715,
  0.07029074047813277, 0.92850900392038, 0.0012002556014871519,
  0.02152438536945611, 0.0455054005583464, 0.9329702140721975,
  0.04906966935755952, 0.2133944547670873, 0.7375358758753532,
  0.17765845029637028, 0.24210251191931964, 0.5802390377843101,
  0.18981235629273674, 0.32719073201917004, 0.4829969116880932,
  0.004458382023289298, 0.14199816693317424, 0.8535434510435365,
  0.08767797648435205, 0.17539639319146172, 0.7369256303241862,
  0.0631803276344105, 0.39213961333441455, 0.5446800590311749,
  0.004149464133923697, 0.33414561503592133, 0.661704920830155,
  0.022794804925916345, 0.17414619605118214, 0.8030589990229016,
  0.02270084437179687, 0.2758390080718242, 0.7014601475563789,
  0.006149648542663977, 0.026222667164652273, 0.9676276842926838,
  0.1120336293422709, 0.24304720236592617, 0.644919168291803,
  0.004781489772987091, 0.22999298405790716, 0.7652255261691058,
  0.06244874217963292, 0.29560828087240165, 0.6419429769479654,
  0.05021118591342799, 0.12139345075409119, 0.8283953633324808,
  0.025727998742878677, 0.3738238003102097, 0.6004482009469116,
  0.005646565993466135, 0.44278340652024356, 0.5515700274862902,
  0.11808906971509514, 0.3377986632005823, 0.5441122670843226,
  0.018242291012294687, 0.09222918919528221, 0.8895285197924231,
  0.0012002556014871768, 0.07029074047813273, 0.92850900392038,
  0.9329702140721975, 0.0455054005583464, 0.02152438536945612,
  0.7375358758753532, 0.2133944547670873, 0.04906966935755949,
  0.5802390377843101, 0.24210251191931964, 0.17765845029637026,
  0.4829969116880932, 0.32719073201917004, 0.1898123562927368,
  0.8535434510435365, 0.14199816693317424, 0.0044583820232893204,
  0.7369256303241862, 0.17539639319146172, 0.08767797648435202,
  0.5446800590311748, 0.39213961333441455, 0.06318032763441064,
  0.661704920830155, 0.33414561503592133, 0.004149464133923672,
  0.8030589990229016, 0.17414619605118214, 0.022794804925916238,
  0.7014601475563789, 0.2758390080718242, 0.022700844371797004,
  0.9676276842926838, 0.026222667164652273, 0.006149648542663968,
  0.644919168291803, 0.24304720236592617, 0.11203362934227094,
  0.7652255261691057, 0.22999298405790716, 0.004781489772987132,
  0.6419429769479654, 0.29560828087240165, 0.062448742179632866,
  0.8283953633324808, 0.12139345075409119, 0.050211185913428096,
  0.6004482009469116, 0.3738238003102097, 0.025727998742878733,
  0.5515700274862902, 0.44278340652024356, 0.005646565993466159,
  0.5441122670843226, 0.3377986632005823, 0.11808906971509502,
  0.8895285197924231, 0.09222918919528221, 0.018242291012294715,
  0.9285090039203802, 0.07029074047813273, 0.0012002556014871519,
  0.02152438536945611, 0.9329702140721975, 0.0455054005583464,
  0.04906966935755952, 0.7375358758753532, 0.2133944547670873,
  0.17765845029637028, 0.5802390377843101, 0.24210251191931964,
  0.18981235629273674, 0.4829969116880932, 0.32719073201917004,
  0.004458382023289298, 0.8535434510435365, 0.14199816693317424,
  0.08767797648435205, 0.7369256303241862, 0.17539639319146172,
  0.0631803276344105, 0.5446800590311749, 0.39213961333441455,
  0.004149464133923697, 0.661704920830155, 0.33414561503592133,
  0.022794804925916345, 0.8030589990229016, 0.17414619605118214,
  0.02270084437179687, 0.7014601475563789, 0.2758390080718242,
  0.006149648542663977, 0.9676276842926838, 0.026222667164652273,
  0.1120336293422709, 0.644919168291803, 0.24304720236592617,
  0.004781489772987091, 0.7652255261691058, 0.22999298405790716,
  0.06244874217963292, 0.6419429769479654, 0.29560828087240165,
  0.05021118591342799, 0.8283953633324808, 0.12139345075409119,
  0.025727998742878677, 0.6004482009469116, 0.3738238003102097,
  0.005646565993466135, 0.5515700274862902, 0.44278340652024356,
  0.11808906971509514, 0.5441122670843226, 0.3377986632005823,
  0.018242291012294687, 0.8895285197924231, 0.09222918919528221,
  0.0012002556014871768, 0.92850900392038, 0.07029074047813273,
  0.0455054005583464, 0.02152438536945612, 0.9329702140721975,
  0.2133944547670873, 0.04906966935755949, 0.7375358758753532,
  0.24210251191931964, 0.17765845029637026, 0.5802390377843101,
  0.32719073201917004, 0.1898123562927368, 0.4829969116880932,
  0.14199816693317424, 0.0044583820232893204, 0.8535434510435365,
  0.17539639319146172, 0.08767797648435202, 0.7369256303241862,
  0.3921396133344145, 0.06318032763441064, 0.5446800590311749,
  0.33414561503592133, 0.004149464133923672, 0.661704920830155,
  0.1741461960511822, 0.022794804925916238, 0.8030589990229016,
  0.27583900807182415, 0.022700844371797004, 0.7014601475563789,
  0.02622266716465227, 0.006149648542663968, 0.9676276842926838,
  0.24304720236592614, 0.11203362934227094, 0.644919168291803,
  0.22999298405790713, 0.004781489772987132, 0.7652255261691058,
  0.29560828087240165, 0.062448742179632866, 0.6419429769479654,
  0.12139345075409114, 0.050211185913428096, 0.8283953633324808,
  0.3738238003102097, 0.025727998742878733, 0.6004482009469116,
  0.4427834065202436, 0.005646565993466159, 0.5515700274862902,
  0.3377986632005824, 0.11808906971509502, 0.5441122670843226,
  0.09222918919528222, 0.018242291012294715, 0.8895285197924231,
  0.07029074047813277, 0.0012002556014871519, 0.92850900392038,
};
const double triangleRule28Weights[] = {
  0.014362466300646136,
  0.0003111352086814963,
  0.008851705010893161,
  0.014210586390448187,
  0.013092748589088966,
  0.007809943371086341,
  0.01354759560332551,
  0.007682110578595024,
  0.011942669640248227,
  0.0051282520046780685,
  0.014362466300646136,
  0.0003111352086814963,
  0.008851705010893161,
  0.014210586390448187,
  0.013092748589088966,
  0.007809943371086341,
  0.01354759560332551,
  0.007682110578595024,
  0.011942669640248227,
  0.0051282520046780685,
  0.014362466300646136,
  0.0003111352086814963,
  0.008851705010893161,
  0.014210586390448187,
  0.013092748589088966,
  0.007809943371086341,
  0.01354759560332551,
  0.007682110578595024,
  0.011942669640248227,
  0.0051282520046780685,
  0.0021175395576808983,
  0.005895672234514246,
  0.012557256216676879,
  0.013106114124099386,
  0.0017788954192555133,
  0.008011929286694964,
  0.008464695734276604,
  0.0023767642676877834,
  0.004276942335017945,
  0.005131277382037297,
  0.0009485404258894006,
  0.0102459865617042,
  0.0023245453644640504,
  0.00892511614027655,
  0.0059178837723538906,
  0.006260534642968552,
  0.0031401776434880364,
  0.0127871384229558,
  0.003204916190793035,
  0.000725134594986083,
  0.0021175395576808983,
  0.005895672234514246,
  0.012557256216676879,
  0.013106114124099386,
  0.0017788954192555133,
  0.008011929286694964,
  0.008464695734276604,
  0.0023767642676877834,
  0.004276942335017945,
  0.005131277382037297,
  0.0009485404258894006,
  0.0102459865617042,
  0.0023245453644640504,
  0.00892511614027655,
  0.0059178837723538906,
  0.006260534642968552,
  0.0031401776434880364,
  0.0127871384229558,
  0.003204916190793035,
  0.000725134594986083,
  0.0021175395576808983,
  0.005895672234514246,
  0.012557256216676879,
  0.013106114124099386,
  0.0017788954192555133,
  0.008011929286694964,
  0.008464695734276604,
  0.0023767642676877834,
  0.004276942335017945,
  0.005131277382037297,
  0.0009485404258894006,
  0.0102459865617042,
  0.0023245453644640504,
  0.00892511614027655,
  0.0059178837723538906,
  0.006260534642968552,
  0.0031401776434880364,
  0.0127871384229558,
  0.003204916190793035,
  0.000725134594986083,
  0.0021175395576808983,
  0.005895672234514246,
  0.012557256216676879,
  0.013106114124099386,
  0.0017788954192555133,
  0.008011929286694964,
  0.008464695734276604,
  0.0023767642676877834,
  0.004276942335017945,
  0.005131277382037297,
  0.0009485404258894006,
  0.0102459865617042,
  0.0023245453644640504,
  0.00892511614027655,
  0.0059178837723538906,
  0.006260534642968552,
  0.0031401776434880364,
  0.0127871384229558,
  0.003204916190793035,
  0.000725134594986083,
  0.0021175395576808983,
  0.005895672234514246,
  0.012557256216676879,
  0.013106114124099386,
  0.0017788954192555133,
  0.008011929286694964,
  0.008464695734276604,
  0.0023767642676877834,
  0.004276942335017945,
  0.005131277382037297,
  0.0009485404258894006,
  0.0102459865617042,
  0.0023245453644640504,
  0.00892511614027655,
  0.0059178837723538906,
  0.006260534642968552,
  0.0031401776434880364,
  0.0127871384229558,
  0.003204916190793035,
  0.000725134594986083,
  0.0021175395576808983,
  0.005895672234514246,
  0.012557256216676879,
  0.013106114124099386,
  0.0017788954192555133,
  0.008011929286694964,
  0.008464695734276604,
  0.0023767642676877834,
  0.004276942335017945,
  0.005131277382037297,
  0.0009485404258894006,
  0.0102459865617042,
  0.0023245453644640504,
  0.00892511614027655,
  0.0059178837723538906,
  0.006260534642968552,
  0.0031401776434880364,
  0.0127871384229558,
  0.003204916190793035,
  0.000725134594986083,
};
const double triangleRule29Points[] = {
  0.0021703507246276788, 0.49891482463768616, 0.49891482463768616,
  0.13123914647653878, 0.4343804267617306, 0.4343804267617306,
  0.9178053287457636, 0.0410973356271182, 0.0410973356271182,
  0.5831893897351982, 0.2084053051324009, 0.2084053051324009,
  0.6785082311360727, 0.16074588443196364, 0.16074588443196364,
  0.023196794134794474, 0.48840160293260276, 0.48840160293260276,
  0.395227177569743, 0.3023864112151285, 0.3023864112151285,
  0.7711463740111488, 0.11442681299442559, 0.11442681299442559,
  0.0704751378385221, 0.46476243108073895, 0.46476243108073895,
  0.8525562372198002, 0.07372188139009989, 0.07372188139009989,
  0.21876164243347251, 0.39061917878326374, 0.39061917878326374,
  0.4989148246376862, 0.49891482463768616, 0.0021703507246276788,
  0.4343804267617306, 0.4343804267617306, 0.13123914647653878,
  0.04109733562711826, 0.0410973356271182, 0.9178053287457636,
  0.20840530513240085, 0.2084053051324009, 0.5831893897351982,
  0.16074588443196358, 0.16074588443196364, 0.6785082311360727,
  0.4884016029326028, 0.48840160293260276, 0.023196794134794474,
  0.30238641121512844, 0.3023864112151285, 0.395227177569743,
  0.11442681299442559, 0.11442681299442559, 0.7711463740111488,
  0.464762431080739, 0.46476243108073895, 0.0704751378385221,
  0.07372188139009994, 0.07372188139009989, 0.8525562372198002,
  0.3906191787832638, 0.39061917878326374, 0.21876164243347251,
  0.4989148246376862, 0.0021703507246276788, 0.49891482463768616,
  0.4343804267617306, 0.13123914647653878, 0.4343804267617306,
  0.04109733562711826, 0.9178053287457636, 0.0410973356271182,
  0.20840530513240085, 0.5831893897351982, 0.2084053051324009,
  0.16074588443196358, 0.6785082311360727, 0.16074588443196364,
  0.4884016029326028, 0.023196794134794474, 0.48840160293260276,
  0.30238641121512844, 0.395227177569743, 0.3023864112151285,
  0.11442681299442559, 0.7711463740111488, 0.11442681299442559,
  0.464762431080739, 0.0704751378385221, 0.46476243108073895,
  0.07372188139009994, 0.8525562372198002, 0.07372188139009989,
  0.3906191787832638, 0.21876164243347251, 0.39061917878326374,
  0.9383291479118497, 0.002728743247921069, 0.058942108840229206,
  0.49303429012347477, 0.15717769986719343, 0.34978801000933185,
  0.6748972098116223, 0.0021009666448275587, 0.32300182354355017,
  0.7736883369367374, 0.06816580881374641, 0.15814585424951613,
  0.9596195731350373, 0.010830958603609348, 0.029549468261353372,
  0.4892484845932905, 0.21893234198017247, 0.29181917342653707,
  0.903190925246271, 0.02128689624073325, 0.0755221785129958,
  0.8420361139149987, 0.040847216576102435, 0.11711666950889889,
  0.987230285395787, 0.001603496496043763, 0.011166218108169191,
  0.6904083654940789, 0.10154598522683399, 0.20804564927908714,
  0.5662628237507425, 0.04152706126882266, 0.39221011498043484,
  0.5464396833448917, 0.0938490411451324, 0.3597112755099759,
  0.7454392707127404, 0.008686029804384135, 0.24587469948287544,
  0.8154081377810313, 0.01758912404404562, 0.16700273817492314,
  0.879467876855841, 0.005523524512212553, 0.11500859863194643,
  0.6607456749400252, 0.0238589269426556, 0.31539539811731915,
  0.7364820152304077, 0.04029533454477179, 0.2232226502248206,
  0.6437257357698205, 0.06787840431144707, 0.2883958599187324,
  0.5930980425461417, 0.13953560718108263, 0.2673663502727756,
  0.5861680189969418, 0.008066585704166612, 0.40576539529889155,
  0.8135558255123531, 0.00012344681228740494, 0.18632072767535954,
  0.05894210884022921, 0.9383291479118497, 0.002728743247921069,
  0.3497880100093318, 0.4930342901234747, 0.15717769986719343,
  0.3230018235435501, 0.6748972098116224, 0.0021009666448275587,
  0.1581458542495161, 0.7736883369367374, 0.06816580881374641,
  0.029549468261353407, 0.9596195731350372, 0.010830958603609348,
  0.2918191734265372, 0.4892484845932904, 0.21893234198017247,
  0.07552217851299581, 0.903190925246271, 0.02128689624073325,
  0.11711666950889887, 0.8420361139149987, 0.040847216576102435,
  0.011166218108169201, 0.987230285395787, 0.001603496496043763,
  0.20804564927908709, 0.6904083654940789, 0.10154598522683399,
  0.3922101149804348, 0.5662628237507425, 0.04152706126882266,
  0.35971127550997595, 0.5464396833448917, 0.0938490411451324,
  0.24587469948287544, 0.7454392707127404, 0.008686029804384135,
  0.16700273817492317, 0.8154081377810312, 0.01758912404404562,
  0.11500859863194646, 0.8794678768558409, 0.005523524512212553,
  0.3153953981173191, 0.6607456749400253, 0.0238589269426556,
  0.22322265022482057, 0.7364820152304077, 0.04029533454477179,
  0.2883958599187324, 0.6437257357698205, 0.06787840431144707,
  0.26736635027277555, 0.5930980425461418, 0.13953560718108263,
  0.40576539529889155, 0.5861680189969418, 0.008066585704166612,
  0.18632072767535957, 0.8135558255123531, 0.00012344681228740494,
  0.0027287432479210505, 0.058942108840229206, 0.9383291479118497,
  0.15717769986719343, 0.34978801000933185, 0.4930342901234747,
  0.0021009666448275066, 0.32300182354355017, 0.6748972098116224,
  0.06816580881374645, 0.15814585424951613, 0.7736883369367374,
  0.010830958603609386, 0.029549468261353372, 0.9596195731350372,
  0.21893234198017253, 0.29181917342653707, 0.4892484845932904,
  0.02128689624073321, 0.0755221785129958, 0.903190925246271,
  0.04084721657610246, 0.11711666950889889, 0.8420361139149987,
  0.0016034964960437437, 0.011166218108169191, 0.987230285395787,
  0.10154598522683389, 0.20804564927908714, 0.6904083654940789,
  0.04152706126882255, 0.39221011498043484, 0.5662628237507425,
  0.09384904114513248, 0.3597112755099759, 0.5464396833448917,
  0.008686029804384154, 0.24587469948287544, 0.7454392707127404,
  0.017589124044045668, 0.16700273817492314, 0.8154081377810312,
  0.0055235245122126075, 0.11500859863194643, 0.8794678768558409,
  0.023858926942655456, 0.31539539811731915, 0.6607456749400253,
  0.040295334544771744, 0.2232226502248206, 0.7364820152304077,
  0.0678784043114471, 0.2883958599187324, 0.6437257357698205,
  0.1395356071810825, 0.2673663502727756, 0.5930980425461418,
  0.008066585704166629, 0.40576539529889155, 0.5861680189969418,
  0.00012344681228737553, 0.18632072767535954, 0.8135558255123531,
  0.9383291479118497, 0.058942108840229206, 0.002728743247921069,
  0.49303429012347477, 0.34978801000933185, 0.15717769986719343,
  0.6748972098116223, 0.32300182354355017, 0.0021009666448275587,
  0.7736883369367374, 0.15814585424951613, 0.06816580881374641,
  0.9596195731350373, 0.029549468261353372, 0.010830958603609348,
  0.4892484845932905, 0.29181917342653707, 0.21893234198017247,
  0.903190925246271, 0.0755221785129958, 0.02128689624073325,
  0.8420361139149987, 0.11711666950889889, 0.040847216576102435,
  0.987230285395787, 0.011166218108169191, 0.001603496496043763,
  0.6904083654940789, 0.20804564927908714, 0.10154598522683399,
  0.5662628237507425, 0.39221011498043484, 0.04152706126882266,
  0.5464396833448917, 0.3597112755099759, 0.0938490411451324,
  0.7454392707127404, 0.24587469948287544, 0.008686029804384135,
  0.8154081377810313, 0.16700273817492314, 0.01758912404404562,
  0.879467876855841, 0.11500859863194643, 0.005523524512212553,
  0.6607456749400252, 0.31539539811731915, 0.0238589269426556,
  0.7364820152304077, 0.2232226502248206, 0.04029533454477179,
  0.6437257357698205, 0.2883958599187324, 0.06787840431144707,
  0.5930980425461417, 0.2673663502727756, 0.13953560718108263,
  0.5861680189969418, 0.40576539529889155, 0.008066585704166612,
  0.8135558255123531, 0.18632072767535954, 0.00012344681228740494,
  0.0027287432479210505, 0.9383291479118497, 0.058942108840229206,
  0.15717769986719343, 0.4930342901234747, 0.34978801000933185,
  0.0021009666448275066, 0.6748972098116224, 0.32300182354355017,
  0.06816580881374645, 0.7736883369367374, 0.15814585424951613,
  0.010830958603609386, 0.9596195731350372, 0.029549468261353372,
  0.21893234198017253, 0.4892484845932904, 0.29181917342653707,
  0.02128689624073321, 0.903190925246271, 0.0755221785129958,
  0.04084721657610246, 0.8420361139149987, 0.11711666950889889,
  0.0016034964960437437, 0.987230285395787, 0.011166218108169191,
  0.10154598522683389, 0.6904083654940789, 0.20804564927908714,
  0.04152706126882255, 0.5662628237507425, 0.39221011498043484,
  0.09384904114513248, 0.5464396833448917, 0.3597112755099759,
  0.008686029804384154, 0.7454392707127404, 0.24587469948287544,
  0.017589124044045668, 0.8154081377810312, 0.16700273817492314,
  0.0055235245122126075, 0.8794678768558409, 0.11500859863194643,
  0.023858926942655456, 0.6607456749400253, 0.31539539811731915,
  0.040295334544771744, 0.7364820152304077, 0.2232226502248206,
  0.0678784043114471, 0.6437257357698205, 0.2883958599187324,
  0.1395356071810825, 0.5930980425461418, 0.2673663502727756,
  0.008066585704166629, 0.5861680189969418, 0.40576539529889155,
  0.00012344681228737553, 0.8135558255123531, 0.18632072767535954,
  0.05894210884022921, 0.002728743247921069, 0.9383291479118497,
  0.3497880100093318, 0.15717769986719343, 0.4930342901234747,
  0.3230018235435501, 0.0021009666448275587, 0.6748972098116224,
  0.1581458542495161, 0.06816580881374641, 0.7736883369367374,
  0.029549468261353407, 0.010830958603609348, 0.9596195731350372,
  0.2918191734265372, 0.21893234198017247, 0.4892484845932904,
  0.07552217851299581, 0.02128689624073325, 0.903190925246271,
  0.11711666950889887, 0.040847216576102435, 0.8420361139149987,
  0.011166218108169201, 0.001603496496043763, 0.987230285395787,
  0.20804564927908709, 0.10154598522683399, 0.6904083654940789,
  0.3922101149804348, 0.04152706126882266, 0.5662628237507425,
  0.35971127550997595, 0.0938490411451324, 0.5464396833448917,
  0.24587469948287544, 0.008686029804384135, 0.7454392707127404,
  0.16700273817492317, 0.01758912404404562, 0.8154081377810312,
  0.11500859863194646, 0.005523524512212553, 0.8794678768558409,
  0.3153953981173191, 0.0238589269426556, 0.6607456749400253,
  0.22322265022482057, 0.04029533454477179, 0.7364820152304077,
  0.2883958599187324, 0.06787840431144707, 0.6437257357698205,
  0.26736635027277555, 0.13953560718108263, 0.5930980425461418,
  0.40576539529889155, 0.008066585704166612, 0.5861680189969418,
  0.18632072767535957, 0.00012344681228740494, 0.8135558255123531,
};
const double triangleRule29Weights[] = {
  0.0015164621031569022,
  0.011171100295167859,
  0.002860491506156887,
  0.012539203442623229,
  0.010571417858227577,
  0.006134401164718911,
  0.016310238807743207,
  0.008172878441227133,
  0.0103131166352585,
  0.005608847132831304,
  0.015913215284088903,
  0.0015164621031569022,
  0.011171100295167859,
  0.002860491506156887,
  0.012539203442623229,
  0.010571417858227577,
  0.006134401164718911,
  0.016310238807743207,
  0.008172878441227133,
  0.0103131166352585,
  0.005608847132831304,
  0.015913215284088903,
  0.0015164621031569022,
  0.011171100295167859,
  0.002860491506156887,
  0.012539203442623229,
  0.010571417858227577,
  0.006134401164718911,
  0.016310238807743207,
  0.008172878441227133,
  0.0103131166352585,
  0.005608847132831304,
  0.015913215284088903,
  0.0007692529714762487,
  0.010452214696922436,
  0.0013528239492524086,
  0.0064391367075338065,
  0.001272194437171631,
  0.013545246572007575,
  0.002761530749590444,
  0.00451268684548733,
  0.0002694922318587012,
  0.009386330676283665,
  0.00782291845830648,
  0.010630396363196614,
  0.0030512388233451906,
  0.003825366671730012,
  0.0017416952313017492,
  0.005669153481665458,
  0.006581997763852206,
  0.009178924164927597,
  0.012518366498834426,
  0.0036413404112807368,
  0.000688672625041761,
  0.0007692529714762487,
  0.010452214696922436,
  0.0013528239492524086,
  0.0064391367075338065,
  0.001272194437171631,
  0.013545246572007575,
  0.002761530749590444,
  0.00451268684548733,
  0.0002694922318587012,
  0.009386330676283665,
  0.00782291845830648,
  0.010630396363196614,
  0.0030512388233451906,
  0.003825366671730012,
  0.0017416952313017492,
  0.005669153481665458,
  0.006581997763852206,
  0.009178924164927597,
  0.012518366498834426,
  0.0036413404112807368,
  0.000688672625041761,
  0.0007692529714762487,
  0.010452214696922436,
  0.0013528239492524086,
  0.0064391367075338065,
  0.001272194437171631,
  0.013545246572007575,
  0.002761530749590444,
  0.00451268684548733,
  0.0002694922318587012,
  0.009386330676283665,
  0.00782291845830648,
  0.010630396363196614,
  0.0030512388233451906,
  0.003825366671730012,
  0.0017416952313017492,
  0.005669153481665458,
  0.006581997763852206,
  0.009178924164927597,
  0.012518366498834426,
  0.0036413404112807368,
  0.000688672625041761,
  0.0007692529714762487,
  0.010452214696922436,
  0.0013528239492524086,
  0.0064391367075338065,
  0.001272194437171631,
  0.013545246572007575,
  0.002761530749590444,
  0.00451268684548733,
  0.0002694922318587012,
  0.009386330676283665,
  0.00782291845830648,
  0.010630396363196614,
  0.0030512388233451906,
  0.003825366671730012,
  0.0017416952313017492,
  0.005669153481665458,
  0.006581997763852206,
  0.009178924164927597,
  0.012518366498834426,
  0.0036413404112807368,
  0.000688672625041761,
  0.0007692529714762487,
  0.010452214696922436,
  0.0013528239492524086,
  0.0064391367075338065,
  0.001272194437171631,
  0.013545246572007575,
  0.002761530749590444,
  0.00451268684548733,
  0.0002694922318587012,
  0.009386330676283665,
  0.00782291845830648,
  0.010630396363196614,
  0.0030512388233451906,
  0.003825366671730012,
  0.0017416952313017492,
  0.005669153481665458,
  0.006581997763852206,
  0.009178924164927597,
  0.012518366498834426,
  0.0036413404112807368,
  0.000688672625041761,
  0.0007692529714762487,
  0.010452214696922436,
  0.0013528239492524086,
  0.0064391367075338065,
  0.001272194437171631,
  0.013545246572007575,
  0.002761530749590444,
  0.00451268684548733,
  0.0002694922318587012,
  0.009386330676283665,
  0.00782291845830648,
  0.010630396363196614,
  0.0030512388233451906,
  0.003825366671730012,
  0.0017416952313017492,
  0.005669153481665458,
  0.006581997763852206,
  0.009178924164927597,
  0.012518366498834426,
  0.0036413404112807368,
  0.000688672625041761,
};
const double triangleRule30Points[] = {
  0.9933625501267107, 0.003318724936644646, 0.003318724936644646,
  0.8552551855506441, 0.07237240722467797, 0.07237240722467797,
  0.905684179515656, 0.047157910242171974, 0.047157910242171974,
  0.06393965269774915, 0.4680301736511254, 0.4680301736511254,
  0.9746267906510645, 0.01268660467446775, 0.01268660467446775,
  0.7568169835545439, 0.12159150822272807, 0.12159150822272807,
  0.6351808769650938, 0.18240956151745308, 0.18240956151745308,
  0.2754254412941003, 0.36228727935294985, 0.36228727935294985,
  0.1265135029030796, 0.4367432485484602, 0.4367432485484602,
  0.4551439184321434, 0.2724280407839283, 0.2724280407839283,
  0.005361321999382884, 0.49731933900030856, 0.49731933900030856,
  0.003318724936644646, 0.003318724936644646, 0.9933625501267107,
  0.07237240722467797, 0.07237240722467797, 0.8552551855506441,
  0.047157910242171974, 0.047157910242171974, 0.905684179515656,
  0.4680301736511254, 0.4680301736511254, 0.06393965269774915,
  0.012686604674467805, 0.01268660467446775, 0.9746267906510645,
  0.12159150822272813, 0.12159150822272807, 0.7568169835545439,
  0.18240956151745302, 0.18240956151745308, 0.6351808769650938,
  0.3622872793529499, 0.36228727935294985, 0.2754254412941003,
  0.43674324854846014, 0.4367432485484602, 0.1265135029030796,
  0.27242804078392835, 0.2724280407839283, 0.4551439184321434,
  0.49731933900030856, 0.49731933900030856, 0.005361321999382884,
  0.003318724936644646, 0.9933625501267107, 0.003318724936644646,
  0.07237240722467797, 0.8552551855506441, 0.07237240722467797,
  0.047157910242171974, 0.905684179515656, 0.047157910242171974,
  0.4680301736511254, 0.06393965269774915, 0.4680301736511254,
  0.012686604674467805, 0.9746267906510645, 0.01268660467446775,
  0.12159150822272813, 0.7568169835545439, 0.12159150822272807,
  0.18240956151745302, 0.6351808769650938, 0.18240956151745308,
  0.3622872793529499, 0.2754254412941003, 0.36228727935294985,
  0.43674324854846014, 0.1265135029030796, 0.4367432485484602,
  0.27242804078392835, 0.4551439184321434, 0.2724280407839283,
  0.49731933900030856, 0.005361321999382884, 0.49731933900030856,
  0.6931109923381601, 0.047835123140772554, 0.25905388452106737,
  0.5287682847771431, 0.07965952693160062, 0.39157218829125634,
  0.5861663154298922, 0.05769340127387423, 0.35614028329623354,
  0.6397260650735271, 0.0772614375768841, 0.2830124973495888,
  0.7356278532534755, 0.022758384295000066, 0.2416137624515244,
  0.6234067740413924, 0.1238119787706746, 0.25278124718793293,
  0.6992119263799823, 0.11588196723610056, 0.18490610638391713,
  0.7397781780644783, 0.0665174447818816, 0.19370437715364014,
  0.9191599701835511, 0.00443878137706136, 0.07640124843938755,
  0.7862883331546218, 0.004663579392688625, 0.20904808745268963,
  0.6967533241762802, 0.004703681764477044, 0.2985429940592427,
  0.6404388932621002, 0.025182066703868706, 0.33437904003403107,
  0.8109926237945619, 0.06577657382474286, 0.12323080238069513,
  0.5353617425851649, 0.12612409498498942, 0.3385141624298457,
  0.4507254468957942, 0.19487095092351842, 0.35440360218068745,
  0.5459302776699086, 0.19100142457228309, 0.2630682977578083,
  0.5379004199107804, 0.027533406124549888, 0.4345661739646696,
  0.8078650909487487, 0.028063921981372968, 0.16407098706987833,
  0.9414155840249849, 0.015902416268934703, 0.0426819997060804,
  0.8787459746951743, 0.027294230652095765, 0.09395979465272987,
  0.8588999350346495, 0.005691211445416102, 0.13540885351993445,
  0.5986161382437196, 0.005162347016621321, 0.3962215147396591,
  0.9699822487416315, 0.000533708660694491, 0.02948404259767394,
  0.25905388452106737, 0.6931109923381601, 0.047835123140772554,
  0.3915721882912563, 0.5287682847771431, 0.07965952693160062,
  0.3561402832962336, 0.5861663154298922, 0.05769340127387423,
  0.2830124973495888, 0.6397260650735271, 0.0772614375768841,
  0.24161376245152444, 0.7356278532534755, 0.022758384295000066,
  0.25278124718793293, 0.6234067740413924, 0.1238119787706746,
  0.18490610638391713, 0.6992119263799823, 0.11588196723610056,
  0.19370437715364008, 0.7397781780644783, 0.0665174447818816,
  0.07640124843938756, 0.9191599701835511, 0.00443878137706136,
  0.20904808745268966, 0.7862883331546218, 0.004663579392688625,
  0.2985429940592427, 0.6967533241762803, 0.004703681764477044,
  0.33437904003403107, 0.6404388932621002, 0.025182066703868706,
  0.12323080238069517, 0.8109926237945619, 0.06577657382474286,
  0.33851416242984567, 0.5353617425851649, 0.12612409498498942,
  0.35440360218068756, 0.4507254468957941, 0.19487095092351842,
  0.26306829775780827, 0.5459302776699086, 0.19100142457228309,
  0.4345661739646697, 0.5379004199107804, 0.027533406124549888,
  0.16407098706987833, 0.8078650909487487, 0.028063921981372968,
  0.04268199970608044, 0.9414155840249848, 0.015902416268934703,
  0.09395979465272986, 0.8787459746951743, 0.027294230652095765,
  0.13540885351993448, 0.8588999350346495, 0.005691211445416102,
  0.39622151473965905, 0.5986161382437196, 0.005162347016621321,
  0.0294840425976739, 0.9699822487416316, 0.000533708660694491,
  0.04783512314077254, 0.25905388452106737, 0.6931109923381601,
  0.0796595269316005, 0.39157218829125634, 0.5287682847771431,
  0.057693401273874345, 0.35614028329623354, 0.5861663154298922,
  0.07726143757688408, 0.2830124973495888, 0.6397260650735271,
  0.0227583842950001, 0.2416137624515244, 0.7356278532534755,
  0.12381197877067462, 0.25278124718793293, 0.6234067740413924,
  0.11588196723610056, 0.18490610638391713, 0.6992119263799823,
  0.06651744478188149, 0.19370437715364014, 0.7397781780644783,
  0.004438781377061329, 0.07640124843938755, 0.9191599701835511,
  0.004663579392688577, 0.20904808745268963, 0.7862883331546218,
  0.004703681764476997, 0.2985429940592427, 0.6967533241762803,
  0.02518206670386869, 0.33437904003403107, 0.6404388932621002,
  0.06577657382474289, 0.12323080238069513, 0.8109926237945619,
  0.12612409498498933, 0.3385141624298457, 0.5353617425851649,
  0.19487095092351847, 0.35440360218068745, 0.4507254468957941,
  0.19100142457228309, 0.2630682977578083, 0.5459302776699086,
  0.02753340612455002, 0.4345661739646696, 0.5379004199107804,
  0.028063921981372975, 0.16407098706987833, 0.8078650909487487,
  0.015902416268934738, 0.0426819997060804, 0.9414155840249848,
  0.027294230652095797, 0.09395979465272987, 0.8787459746951743,
  0.005691211445416067, 0.13540885351993445, 0.8588999350346495,
  0.005162347016621327, 0.3962215147396591, 0.5986161382437196,
  0.0005337086606944652, 0.02948404259767394, 0.9699822487416316,
  0.6931109923381601, 0.25905388452106737, 0.047835123140772554,
  0.5287682847771431, 0.39157218829125634, 0.07965952693160062,
  0.5861663154298922, 0.35614028329623354, 0.05769340127387423,
  0.6397260650735271, 0.2830124973495888, 0.0772614375768841,
  0.7356278532534755, 0.2416137624515244, 0.022758384295000066,
  0.6234067740413924, 0.25278124718793293, 0.1238119787706746,
  0.6992119263799823, 0.18490610638391713, 0.11588196723610056,
  0.7397781780644783, 0.19370437715364014, 0.0665174447818816,
  0.9191599701835511, 0.07640124843938755, 0.00443878137706136,
  0.7862883331546218, 0.20904808745268963, 0.004663579392688625,
  0.6967533241762802, 0.2985429940592427, 0.004703681764477044,
  0.6404388932621002, 0.33437904003403107, 0.025182066703868706,
  0.8109926237945619, 0.12323080238069513, 0.06577657382474286,
  0.5353617425851649, 0.3385141624298457, 0.12612409498498942,
  0.4507254468957942, 0.35440360218068745, 0.19487095092351842,
  0.5459302776699086, 0.2630682977578083, 0.19100142457228309,
  0.5379004199107804, 0.4345661739646696, 0.027533406124549888,
  0.8078650909487487, 0.16407098706987833, 0.028063921981372968,
  0.9414155840249849, 0.0426819997060804, 0.015902416268934703,
  0.8787459746951743, 0.09395979465272987, 0.027294230652095765,
  0.8588999350346495, 0.13540885351993445, 0.005691211445416102,
  0.5986161382437196, 0.3962215147396591, 0.005162347016621321,
  0.9699822487416315, 0.02948404259767394, 0.000533708660694491,
  0.04783512314077254, 0.6931109923381601, 0.25905388452106737,
  0.0796595269316005, 0.5287682847771431, 0.39157218829125634,
  0.057693401273874345, 0.5861663154298922, 0.35614028329623354,
  0.07726143757688408, 0.6397260650735271, 0.2830124973495888,
  0.0227583842950001, 0.7356278532534755, 0.2416137624515244,
  0.12381197877067462, 0.6234067740413924, 0.25278124718793293,
  0.11588196723610056, 0.6992119263799823, 0.18490610638391713,
  0.06651744478188149, 0.7397781780644783, 0.19370437715364014,
  0.004438781377061329, 0.9191599701835511, 0.07640124843938755,
  0.004663579392688577, 0.7862883331546218, 0.20904808745268963,
  0.004703681764476997, 0.6967533241762803, 0.2985429940592427,
  0.02518206670386869, 0.6404388932621002, 0.33437904003403107,
  0.06577657382474289, 0.8109926237945619, 0.12323080238069513,
  0.12612409498498933, 0.5353617425851649, 0.3385141624298457,
  0.19487095092351847, 0.4507254468957941, 0.35440360218068745,
  0.19100142457228309, 0.5459302776699086, 0.2630682977578083,
  0.02753340612455002, 0.5379004199107804, 0.4345661739646696,
  0.028063921981372975, 0.8078650909487487, 0.16407098706987833,
  0.015902416268934738, 0.9414155840249848, 0.0426819997060804,
  0.027294230652095797, 0.8787459746951743, 0.09395979465272987,
  0.005691211445416067, 0.8588999350346495, 0.13540885351993445,
  0.005162347016621327, 0.5986161382437196, 0.3962215147396591,
  0.0005337086606944652, 0.9699822487416316, 0.02948404259767394,
  0.25905388452106737, 0.047835123140772554, 0.6931109923381601,
  0.3915721882912563, 0.07965952693160062, 0.5287682847771431,
  0.3561402832962336, 0.05769340127387423, 0.5861663154298922,
  0.2830124973495888, 0.0772614375768841, 0.6397260650735271,
  0.24161376245152444, 0.022758384295000066, 0.7356278532534755,
  0.25278124718793293, 0.1238119787706746, 0.6234067740413924,
  0.18490610638391713, 0.11588196723610056, 0.6992119263799823,
  0.19370437715364008, 0.0665174447818816, 0.7397781780644783,
  0.07640124843938756, 0.00443878137706136, 0.9191599701835511,
  0.20904808745268966, 0.004663579392688625, 0.7862883331546218,
  0.2985429940592427, 0.004703681764477044, 0.6967533241762803,
  0.33437904003403107, 0.025182066703868706, 0.6404388932621002,
  0.12323080238069517, 0.06577657382474286, 0.8109926237945619,
  0.33851416242984567, 0.12612409498498942, 0.5353617425851649,
  0.35440360218068756, 0.19487095092351842, 0.4507254468957941,
  0.26306829775780827, 0.19100142457228309, 0.5459302776699086,
  0.4345661739646697, 0.027533406124549888, 0.5379004199107804,
  0.16407098706987833, 0.028063921981372968, 0.8078650909487487,
  0.04268199970608044, 0.015902416268934703, 0.9414155840249848,
  0.09395979465272986, 0.027294230652095765, 0.8787459746951743,
  0.13540885351993448, 0.005691211445416102, 0.8588999350346495,
  0.39622151473965905, 0.005162347016621321, 0.5986161382437196,
  0.0294840425976739, 0.000533708660694491, 0.9699822487416316,
};
const double triangleRule30Weights[] = {
  0.00017172990137104944,
  0.003801932668415518,
  0.0028444336676874955,
  0.007784128732330847,
  0.000846550145328889,
  0.007386911834914289,
  0.010752850965432811,
  0.015596091325825796,
  0.012404959028146008,
  0.01491455076268576,
  0.0027913181197407686,
  0.00017172990137104944,
  0.003801932668415518,
  0.0028444336676874955,
  0.007784128732330847,
  0.000846550145328889,
  0.007386911834914289,
  0.010752850965432811,
  0.015596091325825796,
  0.012404959028146008,
  0.01491455076268576,
  0.0027913181197407686,
  0.00017172990137104944,
  0.003801932668415518,
  0.0028444336676874955,
  0.007784128732330847,
  0.000846550145328889,
  0.007386911834914289,
  0.010752850965432811,
  0.015596091325825796,
  0.012404959028146008,
  0.01491455076268576,
  0.0027913181197407686,
  0.004214758463912434,
  0.005924922745092015,
  0.005944220184424487,
  0.006877184387535926,
  0.004092498968347199,
  0.008872654506017345,
  0.007534322929546482,
  0.006804006756101874,
  0.001206696568542118,
  0.0019589485778932435,
  0.0022744459009986784,
  0.00536468484618631,
  0.005870069803065527,
  0.011303023542937487,
  0.01431648526966759,
  0.012926023450118297,
  0.006281596580891664,
  0.004701936994105967,
  0.0018305068761488277,
  0.0038218805470950205,
  0.0019198805574689177,
  0.0026425679231632513,
  0.00033562171146640226,
  0.004214758463912434,
  0.005924922745092015,
  0.005944220184424487,
  0.006877184387535926,
  0.004092498968347199,
  0.008872654506017345,
  0.007534322929546482,
  0.006804006756101874,
  0.001206696568542118,
  0.0019589485778932435,
  0.0022744459009986784,
  0.00536468484618631,
  0.005870069803065527,
  0.011303023542937487,
  0.01431648526966759,
  0.012926023450118297,
  0.006281596580891664,
  0.004701936994105967,
  0.0018305068761488277,
  0.0038218805470950205,
  0.0019198805574689177,
  0.0026425679231632513,
  0.00033562171146640226,
  0.004214758463912434,
  0.005924922745092015,
  0.005944220184424487,
  0.006877184387535926,
  0.004092498968347199,
  0.008872654506017345,
  0.007534322929546482,
  0.006804006756101874,
  0.001206696568542118,
  0.0019589485778932435,
  0.0022744459009986784,
  0.00536468484618631,
  0.005870069803065527,
  0.011303023542937487,
  0.01431648526966759,
  0.012926023450118297,
  0.006281596580891664,
  0.004701936994105967,
  0.0018305068761488277,
  0.0038218805470950205,
  0.0019198805574689177,
  0.0026425679231632513,
  0.00033562171146640226,
  0.004214758463912434,
  0.005924922745092015,
  0.005944220184424487,
  0.006877184387535926,
  0.004092498968347199,
  0.008872654506017345,
  0.007534322929546482,
  0.006804006756101874,
  0.001206696568542118,
  0.0019589485778932435,
  0.0022744459009986784,
  0.00536468484618631,
  0.005870069803065527,
  0.011303023542937487,
  0.01431648526966759,
  0.012926023450118297,
  0.006281596580891664,
  0.004701936994105967,
  0.0018305068761488277,
  0.0038218805470950205,
  0.0019198805574689177,
  0.0026425679231632513,
  0.00033562171146640226,
  0.004214758463912434,
  0.005924922745092015,
  0.005944220184424487,
  0.006877184387535926,
  0.004092498968347199,
  0.008872654506017345,
  0.007534322929546482,
  0.006804006756101874,
  0.001206696568542118,
  0.0019589485778932435,
  0.0022744459009986784,
  0.00536468484618631,
  0.005870069803065527,
  0.011303023542937487,
  0.01431648526966759,
  0.012926023450118297,
  0.006281596580891664,
  0.004701936994105967,
  0.0018305068761488277,
  0.0038218805470950205,
  0.0019198805574689177,
  0.0026425679231632513,
  0.00033562171146640226,
  0.004214758463912434,
  0.005924922745092015,
  0.005944220184424487,
  0.006877184387535926,
  0.004092498968347199,
  0.008872654506017345,
  0.007534322929546482,
  0.006804006756101874,
  0.001206696568542118,
  0.0019589485778932435,
  0.0022744459009986784,
  0.00536468484618631,
  0.005870069803065527,
  0.011303023542937487,
  0.01431648526966759,
  0.012926023450118297,
  0.006281596580891664,
  0.004701936994105967,
  0.0018305068761488277,
  0.0038218805470950205,
  0.0019198805574689177,
  0.0026425679231632513,
  0.00033562171146640226,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double tetrahedronRule1Points[] = {
  0.25, 0.25, 0.25, 0.25,
};
const double tetrahedronRule1Weights[] = {
  1.0,
};
const double tetrahedronRule2Points[] = {
  0.1236668003284584, 0.8215725409676198, 0.03993304864149842, 0.01482761006242336,
  0.4574615870855955, 0.155933120499186, 0.3817653560693467, 0.004839936345871765,
  0.3653145188146345, 0.1800296935103654, 0.006923235573627467, 0.4477325521013727,
  0.0003755150287292757, 0.2160764291848478, 0.4307017070778361, 0.3528463487085868,
};
const double tetrahedronRule2Weights[] = {
  0.1016075484749807,
  0.2787775766865682,
  0.300520939336976,
  0.3190939355014751,
};
const double tetrahedronRule3Points[] = {
  0.6414297914956963, 0.1620014916985245, 0.1838503504920977, 0.01271836631368145,
  0.3454441557197307, 0.01090521221118924, 0.2815238021235462, 0.3621268299455338,
  0.439858947649275, 0.1901170024392839, 0.01140332944455717, 0.3586207204668839,
  0.03787163178235702, 0.170816925164989, 0.1528181430909273, 0.6384932999617267,
  0.1248048621652472, 0.1586851632274406, 0.5856628056552158, 0.1308471689520965,
  0.1414827519695045, 0.5712260521491151, 0.1469183900871696, 0.1403728057942107,
};
const double tetrahedronRule3Weights[] = {
  0.1223220027573451,
  0.1280664127107469,
  0.1325680271444452,
  0.1406244096604032,
  0.2244151669175574,
  0.2520039808095023,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double tetrahedronRule4Points[] = {
  0.1746940586972306, 0.04049050672759043, 0.01356070187980288, 0.7712547326953761,
  0.08140491840285925, 0.752508507009655, 0.06809937093820666, 0.09798720364927911,
  0.7412288820936226, 0.0672232948933834, 0.03518392977359872, 0.1563638932393953,
  0.05334123953574518, 0.419266313879513, 0.04778143555908666, 0.4796110110256551,
  0.4329534904813556, 0.4507658760912768, 0.05945661629943383, 0.05682401712793367,
  0.5380072039161857, 0.1294113737889104, 0.3301904148374645, 0.002391007457439365,
  0.00899126009333578, 0.1215419913339278, 0.3064939884296903, 0.5629727601430461,
  0.1066041725619936, 0.09720464458758327, 0.68439041545304, 0.1118007673973831,
  0.3292329597426469, 0.02956949520647961, 0.3179035602133946, 0.323293984837479,
  0.1038441164109932, 0.4327102390477686, 0.3538232392092971, 0.1096224053319412,
  0.3044484024344968, 0.2402766649280726, 0.126801725915392, 0.3284732067220384,
};
const double tetrahedronRule4Weights[] = {
  0.03925109092483996,
  0.0552733691559369,
  0.05539379887157637,
  0.05993318514655953,
  0.06946996593763537,
  0.07616271524555836,
  0.07942668006802531,
  0.1064680341554901,
  0.1102342324284977,
  0.1549761160162461,
  0.1934108120496345,
};
const double tetrahedronRule5Points[] = {
  0.4544962958743503, 0.4544962958743504, 0.04550370412564962, 0.0455037041256497,
  0.04550370412564967, 0.4544962958743504, 0.4544962958743504, 0.04550370412564958,
  0.04550370412564973, 0.4544962958743503, 0.04550370412564969, 0.4544962958743503,
  0.4544962958743503, 0.04550370412564966, 0.4544962958743504, 0.04550370412564975,
  0.4544962958743503, 0.04550370412564968, 0.04550370412564962, 0.4544962958743505,
  0.0455037041256497, 0.04550370412564966, 0.4544962958743504, 0.4544962958743503,
  0.09273525031089128, 0.7217942490673263, 0.09273525031089122, 0.09273525031089128,
  0.721794249067326, 0.09273525031089128, 0.09273525031089129, 0.0927352503108914,
  0.09273525031089132, 0.09273525031089114, 0.09273525031089129, 0.7217942490673263,
  0.0927352503108913, 0.0927352503108913, 0.7217942490673263, 0.09273525031089103,
  0.3108859192633006, 0.06734224221009831, 0.3108859192633006, 0.3108859192633004,
  0.06734224221009824, 0.3108859192633006, 0.3108859192633007, 0.3108859192633006,
  0.3108859192633006, 0.3108859192633007, 0.3108859192633006, 0.06734224221009805,
  0.3108859192633006, 0.3108859192633007, 0.06734224221009814, 0.3108859192633006,
};
const double tetrahedronRule5Weights[] = {
  0.04254602077708142,
  0.04254602077708145,
  0.04254602077708145,
  0.04254602077708147,
  0.04254602077708147,
  0.04254602077708149,
  0.07349304311636191,
  0.07349304311636191,
  0.07349304311636193,
  0.07349304311636196,
  0.1126879257180158,
  0.1126879257180158,
  0.1126879257180158,
  0.1126879257180159,
};
const double tetrahedronRule6Points[] = {
  0.02431897424814286, 0.03883608434488445, 0.9029287990136113, 0.03391614239336127,
  0.02286582381402311, 0.9037700013321819, 0.02933572108317866, 0.04402845377061632,
  0.008781957777518898, 0.0405760510668179, 0.08860035046891021, 0.8620416406867529,
  0.8411389516623184, 0.05132520616520296, 0.0372647521383555, 0.0702710900341231,
  0.2112976585815863, 0.007354523838069352, 0.2511844952775297, 0.5301633223028146,
  0.02346779557305456, 0.06477516044710505, 0.3908620506710118, 0.5208949933088285,
  0.2130411832361856, 0.06001058302026912, 0.02584268626070331, 0.701105547482842,
  0.2678441981835756, 0.06476943693005288, 0.6367675085585139, 0.03061885632785766,
  0.05399614083591447, 0.2757863004698506, 0.06001614916616868, 0.6102014095280662,
  0.3293797185491983, 0.3251196585770252, 0.3268335046190458, 0.01866711825473061,
  0.6243213635534294, 0.06592492316000995, 0.2535936747432003, 0.05616003854336038,
  0.06319998094256953, 0.6174557201472688, 0.2584491489839256, 0.06089514992623613,
  0.248449540118895, 0.6265402017088824, 0.06211553318359875, 0.06289472498862392,
  0.06373289529499766, 0.277903669330078, 0.5949096890217955, 0.06345374635312873,
  0.06517799276337043, 0.5947173018757956, 0.06660329800760315, 0.2735014073532308,
  0.08367881406005505, 0.06609866241468051, 0.6300545551109896, 0.2201679684142748,
  0.5773457813897267, 0.2877250948264642, 0.06462063807336853, 0.07030848571044053,
  0.038288670738245, 0.3283881712312217, 0.3202874336976925, 0.3130357243328408,
  0.3519391973347045, 0.05509902249072568, 0.3810843089063102, 0.2118774712682597,
  0.5300632754810166, 0.06678959978173812, 0.07699271710096725, 0.326154407636278,
  0.1521038113099309, 0.1246499636374863, 0.201234567364421, 0.5220116576881619,
  0.3041692653497818, 0.3191942803489312, 0.04438334435720821, 0.3322531099440788,
  0.2558207842649862, 0.2794200529459882, 0.269569929633272, 0.1951892331557536,
};
const double tetrahedronRule6Weights[] = {
  0.007095794851659528,
  0.007241276891866975,
  0.01042333572369595,
  0.01592547918500375,
  0.02256566727814283,
  0.02423128687744435,
  0.02550432426704244,
  0.03150940988270644,
  0.03971409764908228,
  0.0432392966954734,
  0.04359039806062918,
  0.04661313412658071,
  0.04714803047226122,
  0.04889007590244217,
  0.04976863009151432,
  0.05303332390816938,
  0.05393501062831199,
  0.05982134766142917,
  0.06261447528131127,
  0.06306636188552053,
  0.06433402197308753,
  0.06713581621255703,
  0.112599404494068,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double tetrahedronRule7Points[] = {
  0.001996825818299818, 0.01920799348858535, 0.6513348958482376, 0.3274602848448772,
  0.06092218458545083, 0.3234568417895977, 0.6151709883118704, 0.0004499853130809361,
  0.0005004334442718418, 0.6355215105837613, 0.0598944722319085, 0.3040835837400583,
  0.6279832293585974, 0.293770036523707, 0.02748237819283441, 0.05076435592486115,
  0.05213668905801093, 0.06201109193664409, 0.05718215451677883, 0.8286700644885661,
  0.8245440666953954, 0.05989419506998693, 0.05677586668994691, 0.05878587154467078,
  0.062815072845237, 0.8207453007415948, 0.05891041282560915, 0.05752921358755903,
  0.6315484739180046, 0.02583316773173042, 0.280405238101906, 0.06221312024835896,
  0.001613532619990097, 0.1991105720528834, 0.2637473753385648, 0.5355285199885618,
  0.3196583760970118, 0.5991009436200256, 0.03521379529745457, 0.04602688498550804,
  0.5508889781422127, 0.2234702025301428, 0.2255285376972644, 0.0001122816303801566,
  0.3505284068372833, 0.003929651487087849, 0.2418446130585829, 0.4036973286170459,
  0.2307849002376704, 0.01403308447330531, 0.5661630745306973, 0.189018940758327,
  0.063969430325799, 0.06247402252315021, 0.812872555571, 0.06068399158005067,
  0.3239480709891824, 0.0624444127129091, 0.5863212858301218, 0.02728623046778667,
  0.2343964973359623, 0.528711306413653, 0.2169982993458658, 0.01989389690451895,
  0.3501153045071709, 0.2615087691765827, 0.01197587688915757, 0.3764000494270889,
  0.2753098106871322, 0.05300013833454678, 0.04497766312688006, 0.6267123878514409,
  0.0762414702839689, 0.03316569983103569, 0.2748015348979936, 0.6157912949870019,
  0.02253298349383202, 0.2604205879982621, 0.5646501024676913, 0.1523963260402146,
  0.04463026790663657, 0.6018235776318118, 0.2899940343655131, 0.0635521200960385,
  0.5990192398798975, 0.0528776293788545, 0.05497958289551413, 0.2931235478457339,
  0.0680111048992614, 0.2977852343835241, 0.04764944310089234, 0.5865542176163221,
  0.1572418559860032, 0.5504559416248597, 0.04374347016073189, 0.2485587322284053,
  0.5003786698498154, 0.2582805473674438, 0.08266909560739215, 0.1586716871753486,
  0.2898612819086906, 0.3971744029949173, 0.1710488778187786, 0.1419154372776134,
  0.1112511334269427, 0.1074624307831534, 0.4758491617393153, 0.3054372740505886,
  0.07400870213911578, 0.4103580959949396, 0.2447616509193416, 0.270871550946603,
  0.2175544442163533, 0.2521305306293954, 0.4487392553835752, 0.08157576977067599,
  0.4372480897645487, 0.1098959763270211, 0.2765716827388576, 0.1762842511695725,
  0.2188126225475045, 0.176438223014948, 0.1757661102664513, 0.4289830441710963,
};
const double tetrahedronRule7Weights[] = {
  0.007708181162000488,
  0.01200379218821986,
  0.01251410745432063,
  0.01670200106364489,
  0.01805707748415785,
  0.0192028117961788,
  0.02059034863228054,
  0.02071208216376285,
  0.0208727051617902,
  0.0210927658418785,
  0.02218031917521178,
  0.02234867148258417,
  0.02241136539539131,
  0.02321680932786219,
  0.0232909869573198,
  0.02456242988597322,
  0.02732991431764643,
  0.02806117831393307,
  0.02831278761193254,
  0.02879628359523458,
  0.03141112745549963,
  0.03379586530275098,
  0.03693580911143848,
  0.04183853160760037,
  0.04299116196398071,
  0.05278166565355367,
  0.06030151559120971,
  0.06418883893545987,
  0.06671120716573174,
  0.06673948942088066,
  0.08233816878056982,
};
const double tetrahedronRule8Points[] = {
  0.0009718783690150193, 0.9573816260583027, 0.01600798423129822, 0.02563851134138408,
  0.01760715612687848, 0.008855594278705747, 0.9485639297990048, 0.02497331979541095,
  0.9408082028316022, 0.0300522477759322, 0.006719678822153188, 0.02241987057031245,
  0.004571184374515704, 0.04868900463902199, 0.0221620710966624, 0.9245777398897999,
  0.4618117251682627, 0.4653151604130365, 0.005422183307178087, 0.06745093111152267,
  0.03576257087872006, 0.5003296720329762, 0.008112050755706058, 0.4557957063325977,
  0.2307434967946494, 0.6113365336918841, 0.005575773030438238, 0.1523441964830283,
  0.02580684887253231, 0.02777675799356541, 0.4665405858909191, 0.4798758072429833,
  0.4139212834388201, 0.4982549617822043, 0.07975787096690573, 0.008065883812069907,
  0.1999067290329215, 0.4794066533528659, 0.3200956067503981, 0.0005910108638145783,
  0.1643869309848081, 0.03985667792342303, 0.0344820754789425, 0.7612743156128263,
  0.03678064973474819, 0.7205111657178718, 0.2043689239073254, 0.03833926064005466,
  0.1890744688700332, 0.03620467192851837, 0.7313673600360894, 0.04335349916535902,
  0.1506377117814253, 0.7623678849544528, 0.05243838992870327, 0.03455601333541851,
  0.2496370830578753, 0.1955460819226021, 0.5417931824618095, 0.01302365255771298,
  0.2579166731543092, 0.2209774649988177, 0.01239592336019548, 0.5087099384866777,
  0.05045500693172469, 0.03938021868450564, 0.1731956086833511, 0.7369691657004186,
  0.7485745607457628, 0.04543453035210961, 0.1632993432993541, 0.04269156560277354,
  0.04648612941109276, 0.1564866850400663, 0.7514965361518376, 0.04553064939700324,
  0.723709495041749, 0.04620058214866413, 0.04349881445195029, 0.1865911083576366,
  0.04908534432749626, 0.04149415901827835, 0.71717735709395, 0.1922431395602754,
  0.7016567760643901, 0.2044918137472231, 0.0468686532808731, 0.04698275690751362,
  0.04478021549603177, 0.719573330071695, 0.05599064468210205, 0.1796558097501712,
  0.4487780077524824, 0.04105029814548231, 0.04568536574611817, 0.4644863283559171,
  0.04312238337787981, 0.4150765842699887, 0.4947991693199913, 0.04700186303214021,
  0.03095052921613287, 0.4246500540795894, 0.1362062412251983, 0.4081931754790795,
  0.2504719219173209, 0.02261090963666046, 0.2224346424927786, 0.5044825259532402,
  0.05438301560623344, 0.2162641488906512, 0.05125376513387382, 0.6780990703692416,
  0.4721332195496732, 0.04544737426285883, 0.4356669945456628, 0.0467524116418051,
  0.03082247209993105, 0.1812621911709453, 0.2593463891596102, 0.5285689475695134,
  0.5111060719135769, 0.02882725890093539, 0.2295407130726556, 0.2305259561128321,
  0.1239784893278184, 0.06224439946102048, 0.4036547750100588, 0.4101223362011024,
  0.3828805011657271, 0.397275457461443, 0.08173362820479114, 0.1381104131680387,
  0.4935900808340203, 0.2161396926300791, 0.03919057319753563, 0.251079653338365,
  0.03383673809722395, 0.2125192261175291, 0.5056419509803703, 0.2480020848048765,
  0.04243030114562282, 0.4862252458661596, 0.2752360272999065, 0.196108425688311,
  0.2502274462930384, 0.04529074988858361, 0.4931447679590647, 0.2113370358593133,
  0.2280801840550788, 0.1425146299088945, 0.1281437397666177, 0.5012614462694089,
  0.4835182802910101, 0.2295406150635747, 0.2420175573174804, 0.0449235473279348,
  0.1822460492233608, 0.4284077707360187, 0.06194696154684466, 0.3273992184937758,
  0.2096423028706461, 0.4853135576380692, 0.1986199776692312, 0.1064241618220535,
  0.1646955059003284, 0.2495207660799524, 0.249905550725755, 0.3358781772939642,
  0.4118962036484124, 0.1582590933458902, 0.2073917351406235, 0.222452967865074,
  0.2003307068778031, 0.2274620499867547, 0.4489545286636978, 0.1232527144717443,
};
const double tetrahedronRule8Weights[] = {
  0.001513945395115064,
  0.001745183535305652,
  0.00207908456701888,
  0.002546900519342975,
  0.00689742831637566,
  0.007521150351860816,
  0.00987651679488672,
  0.01012892125074862,
  0.01186542069707322,
  0.0127993833726196,
  0.01373577255828547,
  0.01471990717542729,
  0.01506376948510308,
  0.01538844541241091,
  0.01561638920378062,
  0.01652936680055228,
  0.01697522925801473,
  0.01738920256251147,
  0.01761253618513347,
  0.01789880380729291,
  0.01798888989785995,
  0.02014671084678948,
  0.02054503634456274,
  0.02192449860652159,
  0.02250456596802116,
  0.02255923875350233,
  0.02274372063450373,
  0.02349892353869306,
  0.02415834392781366,
  0.02513908607058864,
  0.02711753848548565,
  0.02725493593447311,
  0.02818568590000708,
  0.0322412533439274,
  0.03229300064084636,
  0.03272727475354149,
  0.03655009070763308,
  0.0390627099489507,
  0.04009880514133006,
  0.04156749041547345,
  0.0517796239390085,
  0.05286292870602506,
  0.05335380244785541,
  0.05579248779772755,
};
const double tetrahedronRule9Points[] = {
  0.006891366839295159, 0.7203807203359198, 0.2440786635406753, 0.02864924928410972,
  0.1555789083027259, 0.7830238380676567, 0.03722731406074435, 0.02416993956887299,
  0.8847735952623145, 0.03746715582104113, 0.04313984945003826, 0.03461939946660614,
  0.04038577127605769, 0.2233476678136009, 0.723724094807067, 0.01254246610327436,
  0.515285061557277, 0.4405214048473231, 0.03307435692542832, 0.01111917666997152,
  0.03474022441842899, 0.8739842844692827, 0.04802973388725062, 0.04324575722503777,
  0.2737549691522871, 0.5866194063678511, 0.1331737132533926, 0.006451911226469154,
  0.03138783669262657, 0.02302476689782933, 0.2010151099960878, 0.7445722864134563,
  0.04195473200768755, 0.04206648540987851, 0.8751960265284056, 0.04078275605402837,
  0.2133537804622216, 0.01492382397847686, 0.72761122983064, 0.04411116572866158,
  0.05137368203860852, 0.737898449375068, 0.01052487006572961, 0.2002029985205939,
  0.01167918776735336, 0.03967712051591504, 0.47317164143189, 0.4754720502848416,
  0.6123408021820864, 0.1432143403978234, 0.0006662179087437572, 0.2437786395113464,
  0.04585901947602267, 0.04589832979249515, 0.03930065125704704, 0.8689419994744351,
  0.1030115138063945, 0.2313142488715318, 0.002864577988396536, 0.6628096593336771,
  0.00837326895113094, 0.218303550548395, 0.0638376081133778, 0.7094855723870963,
  0.7518893444883036, 0.03020971497018418, 0.03931328269724702, 0.1785876578442652,
  0.2307731120717099, 0.03171156153538288, 0.02914913102984441, 0.7083661953630628,
  0.005807381258551988, 0.4350661767994387, 0.4471841503422259, 0.1119422915997835,
  0.3807370349415273, 0.1946216802654709, 0.4205051742028665, 0.004136110590135245,
  0.2760774398234713, 0.6335347557774519, 0.02029485866160777, 0.07009294573746902,
  0.06107660031735783, 0.4443452478104636, 0.474856882867235, 0.01972126900494353,
  0.04011137824044635, 0.03313166695541811, 0.713691124061697, 0.2130658307424386,
  0.02545934399020729, 0.1809521324516702, 0.6820586129684939, 0.1115299105896286,
  0.6044262999606023, 0.01758681325508173, 0.2037168634602605, 0.1742700233240555,
  0.7098027195586388, 0.04483105915111014, 0.211317992359171, 0.03404822893108,
  0.7304989942620459, 0.1871472921145495, 0.03706986589769196, 0.04528384772571264,
  0.5007701133228333, 0.02448223828136365, 0.04933213970351709, 0.425415508692286,
  0.03332720320375657, 0.4837323966974713, 0.0372285314523825, 0.4457118686463897,
  0.3567521368987188, 0.1328834330395908, 0.02051457140178872, 0.4898498586599018,
  0.1838549978176258, 0.02094427630108402, 0.1704389178072653, 0.6247618080740249,
  0.2268373199643008, 0.4167820833252522, 0.007798392818596213, 0.3485822038918508,
  0.1923717952701477, 0.1242856487305183, 0.6561382235043771, 0.02720433249495668,
  0.3619508813743887, 0.01552011599218286, 0.3924336805270703, 0.2300953221063581,
  0.01965056042084037, 0.6443583098389682, 0.1340945354491865, 0.2018965942910049,
  0.458244669513536, 0.0366754648901354, 0.4635857264004116, 0.04149413919591699,
  0.01538959981066759, 0.3394322940952808, 0.2418695119980843, 0.4033085940959674,
  0.1242356229882021, 0.02743271521385679, 0.4125431242926855, 0.4357885375052556,
  0.5655163520825289, 0.2158455335267193, 0.1861909388269384, 0.03244717556381335,
  0.1031571468282741, 0.6454494634370023, 0.2025517153954042, 0.04884167433931938,
  0.04580873781449243, 0.1306656875755306, 0.2354771046476909, 0.5880484699622861,
  0.2222475737162643, 0.3744969790769868, 0.3639253527626089, 0.03933009444413998,
  0.4587456757955503, 0.360156713211527, 0.03689983110212465, 0.1441977798907981,
  0.3633566801123643, 0.4147619222990371, 0.1625263637506013, 0.0593550338379974,
  0.1839853909173693, 0.05281258992885371, 0.5791440724832208, 0.1840579466705562,
  0.03912033521689179, 0.1799045015970503, 0.4765094010040439, 0.304465762182014,
  0.1524683171735235, 0.1476870681014711, 0.09407076219108002, 0.6057738525339255,
  0.1668749728706788, 0.5729563685802239, 0.07774426835124648, 0.1824243901978508,
  0.1417161598745218, 0.2271598693150327, 0.5175989795285014, 0.113524991281944,
  0.3516091771883741, 0.05503739382968048, 0.1969410619376471, 0.3964123670442984,
  0.3364345271215077, 0.2289840090706933, 0.0827335053473291, 0.35184795846047,
  0.10961245832859, 0.3537003584345384, 0.1179344061919236, 0.418752777044948,
  0.5571603219749478, 0.1325043854190557, 0.1224035951881698, 0.1879316974178267,
  0.08342378852063631, 0.4222286016719213, 0.3031418645744979, 0.1912057452329444,
  0.2709662131081065, 0.3336191905680228, 0.1998230301014543, 0.1955915662224163,
  0.3787443941211687, 0.143482922419707, 0.3469408062547597, 0.1308318772043645,
  0.1819772234774806, 0.1650628409073057, 0.3092464405790883, 0.3437134950361255,
};
const double tetrahedronRule9Weights[] = {
  0.004297209626427251,
  0.005446662686777992,
  0.005501052249840145,
  0.005850159682987847,
  0.006601140555439079,
  0.006741400421625406,
  0.007031651294666076,
  0.007046772694357508,
  0.007093688134910618,
  0.007105780096237482,
  0.007140039716199621,
  0.007199786221046164,
  0.007880140978224906,
  0.008021210535256004,
  0.008198300283729061,
  0.008296235762850181,
  0.00914657068489851,
  0.009165194395294063,
  0.009779402574149908,
  0.009825361104802203,
  0.01031148586360235,
  0.01162495313341008,
  0.01176253653924646,
  0.01257290712247388,
  0.01297525822334384,
  0.01298753113780957,
  0.01308586954308024,
  0.01323110290564774,
  0.01327391604674931,
  0.0132862503909676,
  0.01367723540855299,
  0.0142664460853428,
  0.01489554835071231,
  0.0151187789916045,
  0.0153837327949132,
  0.01571737727344171,
  0.01647539077808772,
  0.01988881060657086,
  0.02135429970991831,
  0.02238071101726632,
  0.02300948922177037,
  0.02529262681684585,
  0.02539251140634734,
  0.02565188198178133,
  0.02628049268374852,
  0.02637558841796568,
  0.02812721864573652,
  0.03184530461010871,
  0.0326397088280212,
  0.033121074422278,
  0.03522036263341143,
  0.03527936474308143,
  0.03571653269823493,
  0.03822108591395342,
  0.04187534771328918,
  0.04521138307921545,
  0.0491021245617486,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double tetrahedronRule10Points[] = {
  0.004844889527768171, 0.004844889527573282, 0.9854653314167374, 0.00484488952792117,
  0.946719848292354, 0.006667080448351054, 0.00806750556190488, 0.03854556569739006,
  0.006667080448658992, 0.03854556569737443, 0.008067505561779886, 0.9467198482921866,
  0.0385455656974801, 0.9467198482918522, 0.008067505562173938, 0.006667080448493744,
  0.00382689193302969, 0.8740251327651677, 0.01855431505435714, 0.1035936602474455,
  0.1035936602480028, 0.003826891933043923, 0.01855431505433685, 0.8740251327646165,
  0.8740251327649323, 0.1035936602475548, 0.01855431505434555, 0.003826891933167313,
  0.01735404744568466, 0.6202583012900509, 0.0324034637009163, 0.3299841875633481,
  0.6202583012898868, 0.3299841875634282, 0.03240346370091293, 0.0173540474457721,
  0.3299841875637114, 0.01735404744578351, 0.03240346370092632, 0.6202583012895788,
  0.03118131875220204, 0.1266394908785819, 0.8114772294984899, 0.03070196087072607,
  0.1266394908788713, 0.03070196087069638, 0.8114772294981942, 0.03118131875223806,
  0.03070196087074504, 0.03118131875221086, 0.8114772294979709, 0.1266394908790732,
  0.7805722458243883, 0.03518958226876812, 0.03307359982554328, 0.1511645720813003,
  0.03518958226870847, 0.1511645720816399, 0.03307359982557704, 0.7805722458240746,
  0.1511645720815177, 0.7805722458241509, 0.03307359982557292, 0.03518958226875854,
  0.8149022829407979, 0.03351563550542005, 0.1193767951360695, 0.03220528641771249,
  0.03351563550541749, 0.03220528641772838, 0.1193767951358615, 0.8149022829409928,
  0.03220528641771444, 0.8149022829405032, 0.1193767951363346, 0.03351563550544774,
  0.5596600888554596, 0.1807602495702272, 0.007438795731167321, 0.2521408658431459,
  0.1807602495700562, 0.2521408658433209, 0.007438795731199615, 0.5596600888554233,
  0.2521408658430335, 0.5596600888557026, 0.007438795731214367, 0.1807602495700495,
  0.03029393775770431, 0.3510309266619137, 0.03266058005326467, 0.5860145555271175,
  0.3510309266617719, 0.5860145555272518, 0.03266058005328976, 0.03029393775768651,
  0.5860145555274775, 0.03029393775772133, 0.03266058005327201, 0.3510309266615292,
  0.03114461249008678, 0.5992738011392268, 0.3365975263830276, 0.0329840599876588,
  0.03298405998767925, 0.03114461249007869, 0.3365975263825117, 0.5992738011397303,
  0.5992738011395161, 0.03298405998767671, 0.3365975263827067, 0.03114461249010042,
  0.01267643164854561, 0.1645472158899154, 0.4090752240119478, 0.4137011284495912,
  0.1645472158900111, 0.4137011284494345, 0.4090752240120063, 0.01267643164854798,
  0.4137011284495361, 0.01267643164855134, 0.4090752240118714, 0.1645472158900412,
  0.03573908441154557, 0.03377912559111834, 0.592532870170714, 0.3379489198266221,
  0.3379489198264275, 0.03573908441154142, 0.5925328701708977, 0.03377912559113339,
  0.03377912559113959, 0.3379489198260952, 0.5925328701712224, 0.03573908441154294,
  0.1336599495323923, 0.1336599495326111, 0.5990201514025275, 0.1336599495324691,
  0.1669597693172063, 0.1669597693175803, 0.4991206920481123, 0.1669597693171012,
  0.0122804285624344, 0.4126008361791699, 0.3979043621857173, 0.1772143730726785,
  0.1772143730727422, 0.01228042856244396, 0.3979043621855937, 0.4126008361792202,
  0.4126008361792021, 0.1772143730727065, 0.3979043621855659, 0.01228042856252548,
  0.3696126448561478, 0.1145379863160246, 0.02495402206716512, 0.4908953467606625,
  0.1145379863158415, 0.4908953467609971, 0.02495402206723796, 0.3696126448559235,
  0.4908953467605529, 0.369612644856217, 0.0249540220672398, 0.1145379863159903,
  0.08302494688196357, 0.7282094809974271, 0.03849678186899388, 0.1502687902516154,
  0.7282094809970688, 0.1502687902517552, 0.03849678186899534, 0.08302494688218064,
  0.1502687902517038, 0.08302494688216776, 0.03849678186896475, 0.7282094809971638,
  0.01680959146959896, 0.4043770144883662, 0.1613371421710751, 0.4174762518709597,
  0.417476251870908, 0.01680959146964861, 0.1613371421710812, 0.4043770144883623,
  0.4043770144883684, 0.4174762518708103, 0.1613371421711606, 0.01680959146966074,
  0.1696138475604023, 0.6339280343903018, 0.1733608592737587, 0.02309725877553723,
  0.02309725877555648, 0.1696138475603947, 0.1733608592737318, 0.633928034390317,
  0.6339280343903569, 0.0230972587755699, 0.1733608592736602, 0.169613847560413,
  0.02434102832026448, 0.6335875653142609, 0.1650530553465075, 0.1770183510189671,
  0.1770183510189467, 0.02434102832027353, 0.1650530553463749, 0.6335875653144049,
  0.6335875653143981, 0.1770183510189177, 0.1650530553463994, 0.02434102832028481,
  0.02935511686037216, 0.1740037654545786, 0.6208415104357218, 0.1757996072493274,
  0.1740037654546278, 0.1757996072492151, 0.6208415104357764, 0.02935511686038061,
  0.1757996072493023, 0.02935511686041814, 0.6208415104356415, 0.174003765454638,
  0.1121243864649791, 0.5325889236500517, 0.2362419588457611, 0.119044731039208,
  0.1190447310392825, 0.112124386465023, 0.2362419588456988, 0.5325889236499958,
  0.5325889236499357, 0.119044731039276, 0.2362419588456608, 0.1121243864651275,
  0.1193225934917416, 0.4534859243589937, 0.1285563923599583, 0.2986350897893064,
  0.2986350897893351, 0.119322593491917, 0.1285563923597633, 0.4534859243589846,
  0.4534859243587895, 0.298635089789364, 0.1285563923599528, 0.1193225934918936,
  0.3020019073266451, 0.3283455214738413, 0.3030261289420949, 0.06662644225741876,
  0.3283455214738281, 0.0666264422574022, 0.3030261289418549, 0.3020019073269148,
  0.06662644225731254, 0.3020019073267441, 0.3030261289420782, 0.3283455214738651,
  0.5159168166142745, 0.1324670107447715, 0.1074464615850585, 0.2441697110558955,
  0.1324670107446421, 0.244169711055904, 0.1074464615851541, 0.5159168166142998,
  0.2441697110556646, 0.5159168166144414, 0.1074464615851919, 0.132467010744702,
  0.318206200820324, 0.3182062008205924, 0.04538139753862875, 0.3182062008204549,
  0.1207131116358087, 0.3395130626211381, 0.4110926574948671, 0.1286811682481862,
  0.3395130626209017, 0.1286811682481305, 0.4110926574949583, 0.1207131116360095,
  0.1286811682481935, 0.1207131116358556, 0.4110926574950111, 0.3395130626209398,
  0.2570719807624278, 0.2570719807625507, 0.2287840577124626, 0.257071980762559,
};
const double tetrahedronRule10Weights[] = {
  0.00038191631629908,
  0.0007900991147457261,
  0.000790099114751852,
  0.0007900991147566522,
  0.001692565839144685,
  0.001692565839147159,
  0.001692565839155852,
  0.006139154239825477,
  0.006139154239845127,
  0.00613915423984776,
  0.006620345902485029,
  0.006620345902488165,
  0.006620345902492523,
  0.00698496100499754,
  0.006984961005002381,
  0.006984961005003632,
  0.007148771454639654,
  0.00714877145464187,
  0.007148771454646738,
  0.008212047324810415,
  0.008212047324821453,
  0.008212047324823316,
  0.009137979936199884,
  0.00913797993620436,
  0.009137979936209432,
  0.01017498609134363,
  0.01017498609134559,
  0.01017498609135072,
  0.01124219135089412,
  0.01124219135090164,
  0.0112421913509066,
  0.01139221858501813,
  0.01139221858502278,
  0.01139221858502423,
  0.01141697336749778,
  0.01175510589206867,
  0.01181696318891137,
  0.01181696318891984,
  0.01181696318895197,
  0.01238796466594707,
  0.01238796466597009,
  0.01238796466597345,
  0.01250347900028499,
  0.01250347900029171,
  0.01250347900029996,
  0.01256811590621936,
  0.01256811590623869,
  0.01256811590625165,
  0.01314851816663448,
  0.01314851816663657,
  0.01314851816664407,
  0.01370670468173037,
  0.01370670468173512,
  0.01370670468173877,
  0.01666442945505318,
  0.01666442945505708,
  0.01666442945507699,
  0.02067059333601017,
  0.0206705933360491,
  0.02067059333605243,
  0.02540707585115189,
  0.02540707585115704,
  0.02540707585116386,
  0.02682694483770256,
  0.02682694483770887,
  0.02682694483771208,
  0.02732329919496712,
  0.02732329919497055,
  0.02732329919498021,
  0.02791156768822412,
  0.02809256245491682,
  0.02809256245494129,
  0.02809256245494643,
  0.04657852198441921,
};
const double tetrahedronRule11Points[] = {
  0.02174356161974667, 0.02174356162123492, 0.9347693151393625, 0.02174356161965596,
  0.01214887718924207, 0.4733927262830146, 0.5068373557636653, 0.007621040764078102,
  0.473392726282396, 0.007621040764793446, 0.5068373557636205, 0.01214887718919,
  0.007621040764693851, 0.01214887718929203, 0.5068373557640636, 0.4733927262819505,
  0.8283411311394426, 0.01186743374839475, 0.03349202862194989, 0.1262994064902127,
  0.1262994064902889, 0.8283411311393326, 0.03349202862186627, 0.0118674337485122,
  0.01186743374856977, 0.1262994064902864, 0.03349202862190801, 0.8283411311392358,
  0.03884286462495556, 0.0266245121640002, 0.02791260212206558, 0.9066200210889787,
  0.906620021088922, 0.03884286462496065, 0.02791260212209652, 0.0266245121640208,
  0.02662451216400466, 0.9066200210888388, 0.02791260212224616, 0.03884286462491044,
  0.01779838979231115, 0.02570671787901103, 0.1452959108855631, 0.8111989814431148,
  0.8111989814430212, 0.01779838979236296, 0.1452959108856611, 0.02570671787895482,
  0.02570671787902293, 0.8111989814422269, 0.1452959108864052, 0.01779838979234497,
  0.4336893678654693, 0.03413212384063684, 0.004124974507952623, 0.5280535337859413,
  0.5280535337860727, 0.4336893678650325, 0.0041249745082621, 0.03413212384063269,
  0.03413212384056524, 0.528053533786363, 0.004124974508272195, 0.4336893678647996,
  0.02723844389731109, 0.02928619896418311, 0.8221371579049448, 0.1213381992335609,
  0.1213381992336525, 0.02723844389723012, 0.8221371579047962, 0.02928619896432116,
  0.0292861989645277, 0.1213381992371994, 0.8221371579007392, 0.02723844389753383,
  0.1055219304212634, 0.4058583387143239, 0.4825471524757858, 0.006072578388626904,
  0.40585833871604, 0.006072578389145572, 0.4825471524736373, 0.1055219304211772,
  0.00607257838916173, 0.1055219304213615, 0.482547152473874, 0.4058583387156028,
  0.7375158260909277, 0.09328386025279926, 0.01187574741300857, 0.1573245662432645,
  0.09328386025323457, 0.1573245662432324, 0.01187574741303624, 0.7375158260904968,
  0.1573245662429647, 0.7375158260902062, 0.01187574741367739, 0.0932838602531518,
  0.7570556764755156, 0.1851613866917053, 0.02607843400608577, 0.03170450282669325,
  0.1851613866916737, 0.03170450282669195, 0.02607843400609957, 0.7570556764755348,
  0.0317045028266906, 0.7570556764755849, 0.02607843400619944, 0.1851613866915251,
  0.3085734208212338, 0.6353194772067751, 0.03266098603990054, 0.02344611593209055,
  0.635319477206719, 0.02344611593205012, 0.03266098604008431, 0.3085734208211466,
  0.02344611593211183, 0.3085734208211992, 0.03266098603998926, 0.6353194772066998,
  0.02841949702328586, 0.2801664445485925, 0.6575245517573061, 0.03388950667081558,
  0.2801664445453317, 0.03388950667075014, 0.6575245517602716, 0.02841949702364654,
  0.03388950667083485, 0.02841949702363653, 0.6575245517604836, 0.2801664445450449,
  0.7288732494846533, 0.1160230818544248, 0.1355923645754941, 0.01951130408542781,
  0.1160230818543114, 0.01951130408545599, 0.1355923645754723, 0.7288732494847604,
  0.01951130408539934, 0.7288732494841443, 0.135592364576106, 0.1160230818543503,
  0.144054962296286, 0.680860745134503, 0.1577793967317463, 0.0173048958374647,
  0.01730489583748775, 0.1440549622963796, 0.1577793967318802, 0.6808607451342525,
  0.6808607451345954, 0.01730489583762223, 0.157779396731644, 0.1440549622961383,
  0.1579550425986422, 0.01216008923516082, 0.6749562807643449, 0.1549285874018521,
  0.1549285874017353, 0.1579550425979384, 0.6749562807650454, 0.01216008923528078,
  0.01216008923534246, 0.1549285874013449, 0.6749562807649698, 0.1579550425983428,
  0.01001242225693271, 0.4226210458987284, 0.4504683351507885, 0.1168981966935504,
  0.1168981966933887, 0.01001242225711663, 0.4504683351504025, 0.4226210458990921,
  0.4226210458990461, 0.1168981966933672, 0.4504683351504458, 0.010012422257141,
  0.5566694034765993, 0.3465053726509192, 0.07740138872102775, 0.01942383515145374,
  0.01942383515147987, 0.5566694034766593, 0.07740138872115238, 0.3465053726507085,
  0.3465053726511215, 0.01942383515155061, 0.07740138872070887, 0.556669403476619,
  0.613355585987273, 0.03707747991970328, 0.3147249103897943, 0.03484202370322936,
  0.037077479919721, 0.03484202370319439, 0.3147249103898168, 0.6133555859872678,
  0.0348420237032176, 0.6133555859856407, 0.314724910391352, 0.03707747991978971,
  0.3389609703820722, 0.01688864018974739, 0.280802863730256, 0.3633475256979243,
  0.01688864018976847, 0.3633475256969008, 0.280802863730816, 0.3389609703825148,
  0.3633475256976239, 0.3389609703821428, 0.2808028637303945, 0.01688864018983882,
  0.2689933017087768, 0.1524656156298647, 0.02218921323001911, 0.5563518694313393,
  0.5563518694315872, 0.2689933017084892, 0.0221892132299926, 0.152465615629931,
  0.1524656156298783, 0.5563518694313629, 0.02218921323010947, 0.2689933017086493,
  0.3277711127242067, 0.3277711127240469, 0.01668666182758015, 0.3277711127241663,
  0.4945020621274046, 0.02951774250327373, 0.2969980096590332, 0.1789821857102886,
  0.02951774250352841, 0.1789821857098627, 0.2969980096594547, 0.494502062127154,
  0.1789821857092536, 0.4945020621265333, 0.2969980096607454, 0.02951774250346773,
  0.1978395470663011, 0.02960272586703677, 0.2278827225106128, 0.5446750045560493,
  0.02960272586707343, 0.544675004555141, 0.2278827225112254, 0.1978395470665602,
  0.5446750045559754, 0.1978395470660405, 0.2278827225108745, 0.02960272586710963,
  0.03229881331828368, 0.3371690700776922, 0.1320500662715863, 0.4984820503324378,
  0.4984820503323908, 0.03229881331833241, 0.1320500662716444, 0.3371690700776324,
  0.3371690700771687, 0.4984820503329197, 0.1320500662716443, 0.0322988133182672,
  0.1207512536386751, 0.6778351364529377, 0.1011781353097973, 0.1002354745985899,
  0.6778351364538195, 0.1002354745986857, 0.1011781353085159, 0.1207512536389788,
  0.1002354745985345, 0.1207512536390304, 0.1011781353086743, 0.6778351364537608,
  0.138106941917413, 0.3354607968315433, 0.03273663417213666, 0.493695627078907,
  0.4936956270790593, 0.1381069419173125, 0.03273663417222188, 0.3354607968314063,
  0.3354607968314335, 0.4936956270789277, 0.03273663417220138, 0.1381069419174373,
  0.2500532412376334, 0.2507616099201166, 0.4585809066512544, 0.04060424219099551,
  0.2507616099209062, 0.04060424219100611, 0.4585809066503929, 0.2500532412376947,
  0.04060424219112386, 0.2500532412374494, 0.4585809066512888, 0.2507616099201379,
  0.09261674502310314, 0.3090936802353301, 0.5079960391158374, 0.0902935356257294,
  0.3090936802365318, 0.0902935356263497, 0.5079960391138479, 0.09261674502327055,
  0.09029353562658468, 0.09261674502301917, 0.5079960391137064, 0.3090936802366897,
  0.1139695348123683, 0.1139695348116085, 0.6580913955636913, 0.1139695348123319,
  0.1429946401664338, 0.2384743646845937, 0.1443488665029351, 0.4741821286460375,
  0.4741821286458542, 0.1429946401665482, 0.1443488665032992, 0.2384743646842984,
  0.2384743646842464, 0.4741821286455784, 0.1443488665038495, 0.1429946401663257,
  0.2864949113772423, 0.1115967035331357, 0.1108203324715355, 0.4910880526180866,
  0.1115967035330135, 0.4910880526179628, 0.1108203324717666, 0.2864949113772571,
  0.4910880526178663, 0.286494911377532, 0.1108203324716498, 0.111596703532952,
  0.125536113167282, 0.1148821967817834, 0.2994703853758982, 0.4601113046750364,
  0.4601113046750214, 0.1255361131668398, 0.2994703853761758, 0.1148821967819631,
  0.1148821967814947, 0.4601113046733321, 0.299470385377665, 0.1255361131675082,
  0.1968268645044536, 0.1968268645044899, 0.4095194064864269, 0.1968268645046297,
  0.1275456273615645, 0.3107744236691848, 0.2609901451138755, 0.3006898038553752,
  0.3107744236696469, 0.3006898038543989, 0.2609901451144841, 0.1275456273614701,
  0.3006898038549698, 0.1275456273614465, 0.260990145113821, 0.3107744236697628,
  0.296008469913471, 0.2960084699134847, 0.1119745902596869, 0.2960084699133574,
};
const double tetrahedronRule11Weights[] = {
  0.001111230465888245,
  0.001463529470322484,
  0.001463529470382294,
  0.001463529470386782,
  0.002655926879312198,
  0.002655926879322708,
  0.002655926879333268,
  0.002793764937916421,
  0.002793764937921083,
  0.002793764937931147,
  0.003167952255785238,
  0.00316795225578531,
  0.003167952255806052,
  0.003270326156741943,
  0.003270326156781258,
  0.003270326156784528,
  0.004339611139614775,
  0.004339611139623161,
  0.004339611139720208,
  0.005113551260037138,
  0.005113551260179199,
  0.005113551260189843,
  0.005142497687335369,
  0.005142497687344614,
  0.005142497687469521,
  0.006077053503557707,
  0.006077053503558295,
  0.006077053503578441,
  0.006077208769493818,
  0.006077208769512546,
  0.006077208769514417,
  0.006333977981799393,
  0.006333977981935039,
  0.006333977981939412,
  0.006372925303353713,
  0.006372925303359109,
  0.00637292530337129,
  0.007018558826226705,
  0.007018558826230605,
  0.007018558826244519,
  0.007201764440985961,
  0.007201764440986914,
  0.007201764441015829,
  0.007225542757473971,
  0.007225542757538953,
  0.007225542757541352,
  0.008304891684153702,
  0.008304891684155838,
  0.008304891684182603,
  0.009030934609166132,
  0.009030934609173119,
  0.009030934609209975,
  0.009764991542963978,
  0.009764991542989192,
  0.009764991543035607,
  0.01124224327790999,
  0.01124224327791498,
  0.01124224327794794,
  0.01163750798423778,
  0.01169779583413261,
  0.01169779583418422,
  0.01169779583429073,
  0.01242902474833788,
  0.01242902474834883,
  0.01242902474835196,
  0.01289883963468391,
  0.01289883963468869,
  0.01289883963470812,
  0.01520459535499074,
  0.01520459535499386,
  0.01520459535500037,
  0.01558272282728873,
  0.0155827228273156,
  0.0155827228273276,
  0.0173573262920914,
  0.01735732629212318,
  0.01735732629215922,
  0.01741083395204449,
  0.01741083395206623,
  0.01741083395208139,
  0.01799622751493549,
  0.01969180309262242,
  0.01969180309266106,
  0.01969180309277878,
  0.0200503514292504,
  0.02005035142926104,
  0.02005035142929472,
  0.02164912272125193,
  0.02164912272126182,
  0.02164912272129781,
  0.02702858870559996,
  0.02758428230058713,
  0.02758428230059255,
  0.02758428230059998,
  0.02976459331262114,
};
const double tetrahedronRule12Points[] = {
  0.005336077019643312, 0.00533607701965122, 0.9839917689410563, 0.00533607701964911,
  0.02289609338296681, 0.9546184848667337, 0.01790586600742269, 0.004579555742876745,
  0.004579555742875841, 0.0228960933829682, 0.0179058660074233, 0.9546184848667327,
  0.9546184848667292, 0.004579555742878448, 0.0179058660074248, 0.02289609338296758,
  0.003634038039874281, 0.8589044391845247, 0.01981617795956102, 0.11764534481604,
  0.1176453448160352, 0.003634038039875694, 0.01981617795956089, 0.8589044391845282,
  0.858904439184522, 0.1176453448160376, 0.01981617795956242, 0.003634038039877985,
  0.03542041822023295, 0.5224715513554079, 0.01083320231284623, 0.431274828111513,
  0.5224715513554018, 0.4312748281115071, 0.01083320231285078, 0.03542041822024034,
  0.43127482811151, 0.03542041822023723, 0.01083320231285082, 0.522471551355402,
  0.7939888499122254, 0.003557095377268929, 0.03305477917755645, 0.1693992755329492,
  0.003557095377268694, 0.1693992755329503, 0.0330547791775573, 0.7939888499122237,
  0.1693992755329477, 0.7939888499122263, 0.0330547791775572, 0.003557095377268754,
  0.03490045658756769, 0.002190912398338879, 0.6722668687771673, 0.2906417622369261,
  0.2906417622369189, 0.03490045658756785, 0.6722668687771728, 0.002190912398340461,
  0.002190912398345305, 0.2906417622369231, 0.6722668687771658, 0.03490045658756569,
  0.2341448840740503, 0.692501417588051, 0.0005245712210146334, 0.0728291271168841,
  0.07282912711688336, 0.2341448840740487, 0.000524571221016469, 0.6925014175880515,
  0.6925014175880473, 0.07282912711688572, 0.0005245712210174548, 0.2341448840740495,
  0.3050609665772057, 0.01338905088310755, 0.02647035150983993, 0.6550796310298468,
  0.6550796310298418, 0.3050609665772103, 0.02647035150984013, 0.01338905088310775,
  0.01338905088311035, 0.6550796310298342, 0.02647035150984075, 0.3050609665772147,
  0.004307832160712481, 0.09910993965985174, 0.1523437205162723, 0.7442385076631635,
  0.09910993965985478, 0.7442385076631619, 0.1523437205162712, 0.004307832160712038,
  0.7442385076631638, 0.004307832160714106, 0.1523437205162691, 0.09910993965985301,
  0.05919699437842132, 0.07116099648149783, 0.01765696019083371, 0.8519850489492471,
  0.07116099648149686, 0.8519850489492479, 0.01765696019083371, 0.05919699437842155,
  0.851985048949244, 0.05919699437842153, 0.01765696019083469, 0.07116099648149979,
  0.06123548744419532, 0.2324179989563869, 0.6975189009523872, 0.00882761264703058,
  0.00882761264703291, 0.06123548744418655, 0.6975189009523861, 0.2324179989563944,
  0.2324179989563872, 0.008827612647035132, 0.6975189009523897, 0.06123548744418805,
  0.09851040146030474, 0.02461521681961515, 0.8525144716501452, 0.02435991006993499,
  0.02461521681961598, 0.02435991006993637, 0.8525144716501353, 0.09851040146031231,
  0.02435991006993612, 0.09851040146031514, 0.8525144716501323, 0.02461521681961654,
  0.0299575541295916, 0.4833426975320538, 0.4764936746832871, 0.01020607365506754,
  0.0102060736550687, 0.02995755412959167, 0.4764936746832857, 0.483342697532054,
  0.4833426975320467, 0.01020607365507009, 0.4764936746832923, 0.02995755412959084,
  0.6941399725295285, 0.02362764131444302, 0.2643810815068189, 0.01785130464920953,
  0.0178513046492101, 0.6941399725295325, 0.2643810815068127, 0.02362764131444467,
  0.02362764131444548, 0.01785130464921, 0.2643810815068133, 0.6941399725295312,
  0.03438582765934707, 0.02349501300003503, 0.0990866132622732, 0.8430325460783448,
  0.02349501300003591, 0.8430325460783443, 0.09908661326227276, 0.03438582765934704,
  0.8430325460783392, 0.03438582765934772, 0.09908661326227759, 0.02349501300003547,
  0.3771063994176174, 0.5748727589136075, 0.0304912794861778, 0.01752956218259738,
  0.5748727589136118, 0.01752956218259882, 0.03049127948617824, 0.3771063994176111,
  0.01752956218260132, 0.3771063994176133, 0.03049127948617957, 0.5748727589136059,
  0.3324969599766356, 0.3324969599766495, 0.002509120070074782, 0.3324969599766401,
  0.1624334612403688, 0.3425319979501514, 0.4858624607394064, 0.009172080070073307,
  0.3425319979501512, 0.009172080070074445, 0.4858624607394076, 0.1624334612403668,
  0.009172080070074595, 0.1624334612403718, 0.48586246073941, 0.3425319979501437,
  0.1021695690942893, 0.0288780033877441, 0.2474312436355633, 0.6215211838824033,
  0.02887800338774448, 0.6215211838824055, 0.2474312436355594, 0.1021695690942906,
  0.6215211838824011, 0.1021695690942831, 0.2474312436355717, 0.02887800338774416,
  0.1183429008210087, 0.5459504609989174, 0.3155723028572613, 0.02013433532281261,
  0.02013433532281294, 0.1183429008210102, 0.31557230285726, 0.5459504609989169,
  0.5459504609989215, 0.02013433532281465, 0.3155723028572566, 0.1183429008210072,
  0.4641610608049748, 0.08568157353024372, 0.4268281867514006, 0.02332917891338077,
  0.0233291789133806, 0.4641610608049873, 0.4268281867513944, 0.0856815735302377,
  0.08568157353024217, 0.02332917891338057, 0.4268281867513945, 0.4641610608049827,
  0.4810426322698022, 0.2337921730578832, 0.2697819249825928, 0.01538326968972176,
  0.01538326968972469, 0.4810426322698028, 0.2697819249825922, 0.2337921730578804,
  0.2337921730578815, 0.01538326968972496, 0.2697819249825896, 0.481042632269804,
  0.08312515611213879, 0.6898395103699005, 0.02408109553674171, 0.202954237981219,
  0.20295423798122, 0.08312515611213996, 0.02408109553674232, 0.6898395103698977,
  0.6898395103698945, 0.2029542379812216, 0.02408109553674225, 0.08312515611214158,
  0.02742002486773186, 0.1526139134707651, 0.7016489041188455, 0.1183171575426576,
  0.1526139134707658, 0.1183171575426507, 0.7016489041188496, 0.02742002486773387,
  0.1183171575426545, 0.02742002486773273, 0.7016489041188465, 0.1526139134707662,
  0.0256118593510928, 0.6956093147224817, 0.1154478712992354, 0.1633309546271902,
  0.1633309546271897, 0.02561185935109283, 0.1154478712992363, 0.6956093147224812,
  0.695609314722476, 0.1633309546271908, 0.1154478712992393, 0.02561185935109389,
  0.2708902039289692, 0.5606658837700146, 0.1501625601277951, 0.01828135217322113,
  0.5606658837700202, 0.01828135217322237, 0.1501625601277912, 0.2708902039289662,
  0.01828135217322301, 0.2708902039289658, 0.1501625601277926, 0.5606658837700186,
  0.6014420504489564, 0.07656778420928108, 0.06193417797899343, 0.2600559873627691,
  0.2600559873627669, 0.6014420504489668, 0.06193417797899366, 0.0765677842092726,
  0.0765677842092839, 0.2600559873627518, 0.06193417797899652, 0.6014420504489678,
  0.07462605132720868, 0.128036327678861, 0.0802610178929508, 0.7170766031009794,
  0.7170766031009705, 0.0746260513272115, 0.08026101789294995, 0.128036327678868,
  0.1280363276788657, 0.7170766031009719, 0.08026101789294988, 0.07462605132721249,
  0.1859004086837668, 0.01925270365058326, 0.5025986233550219, 0.292248264310628,
  0.2922482643106227, 0.185900408683766, 0.5025986233550276, 0.01925270365058374,
  0.01925270365058409, 0.2922482643106334, 0.5025986233550225, 0.18590040868376,
  0.1176843397145563, 0.1176843397145589, 0.6469469808563281, 0.1176843397145567,
  0.2114376345514575, 0.2363780333382985, 0.02542476511605016, 0.5267595669941939,
  0.5267595669941891, 0.211437634551462, 0.02542476511605067, 0.2363780333382982,
  0.2363780333382918, 0.5267595669941991, 0.02542476511605207, 0.211437634551457,
  0.4463155182649424, 0.4028816246284508, 0.02619956075625247, 0.1246032963503544,
  0.402881624628445, 0.1246032963503558, 0.02619956075625247, 0.4463155182649468,
  0.1246032963503482, 0.4463155182649512, 0.02619956075625223, 0.4028816246284483,
  0.06201821930268873, 0.08004502188860088, 0.5617139637207647, 0.2962227950879458,
  0.2962227950879483, 0.06201821930269108, 0.5617139637207541, 0.08004502188860652,
  0.08004502188860683, 0.2962227950879417, 0.5617139637207641, 0.06201821930268736,
  0.2972901553171066, 0.3803360632262429, 0.297442217416377, 0.02493156404027352,
  0.3803360632262462, 0.02493156404027269, 0.2974422174163724, 0.2972901553171086,
  0.02493156404027382, 0.2972901553171099, 0.297442217416373, 0.3803360632262432,
  0.6021485466361711, 0.0799434865871736, 0.1972600853341152, 0.12064788144254,
  0.120647881442539, 0.6021485466361716, 0.1972600853341229, 0.07994348658716655,
  0.07994348658717083, 0.1206478814425371, 0.1972600853341221, 0.6021485466361699,
  0.02875584715397042, 0.4891098147268006, 0.1151244443817293, 0.3670098937374996,
  0.3670098937375008, 0.02875584715397076, 0.1151244443817276, 0.4891098147268008,
  0.4891098147267995, 0.3670098937374994, 0.1151244443817297, 0.02875584715397138,
  0.134993927609458, 0.4106933140901517, 0.3647602491933826, 0.08955250910700774,
  0.08955250910700893, 0.1349939276094596, 0.3647602491933785, 0.410693314090153,
  0.4106933140901513, 0.08955250910701389, 0.3647602491933695, 0.1349939276094653,
  0.3918753971997565, 0.114767516763099, 0.2334539319513102, 0.2599031540858343,
  0.2599031540858343, 0.3918753971997636, 0.2334539319513043, 0.1147675167630978,
  0.1147675167631061, 0.2599031540858358, 0.2334539319513023, 0.3918753971997558,
  0.1301270947620232, 0.3163617622563091, 0.1273831687260135, 0.4261279742556542,
  0.3163617622563013, 0.426127974255657, 0.1273831687260152, 0.1301270947620265,
  0.4261279742556524, 0.1301270947620246, 0.127383168726021, 0.316361762256302,
  0.4045023685632761, 0.2089114968404676, 0.2918235155672437, 0.09476261902901267,
  0.2089114968404671, 0.09476261902901918, 0.2918235155672501, 0.4045023685632637,
  0.0947626190290201, 0.4045023685632663, 0.2918235155672511, 0.2089114968404626,
  0.2274485368045121, 0.1002497543721358, 0.4514599495099783, 0.2208417593133737,
  0.1002497543721362, 0.2208417593133712, 0.4514599495099766, 0.227448536804516,
  0.2208417593133764, 0.2274485368045148, 0.4514599495099708, 0.1002497543721381,
  0.5075486051202548, 0.2316476952172538, 0.1266237132343918, 0.1341799864280997,
  0.1341799864280956, 0.5075486051202593, 0.126623713234395, 0.2316476952172501,
  0.231647695217251, 0.1341799864280973, 0.1266237132343931, 0.5075486051202587,
  0.3053295843360563, 0.305329584336061, 0.08401124699181982, 0.3053295843360628,
  0.2482123715562289, 0.2482123715562241, 0.2553628853313281, 0.248212371556219,
};
const double tetrahedronRule12Weights[] = {
  0.0002001999422360427,
  0.0005057428796402097,
  0.0005057428796402238,
  0.0005057428796403027,
  0.001289456072169969,
  0.001289456072170008,
  0.001289456072170193,
  0.002086301293239566,
  0.002086301293240483,
  0.002086301293240565,
  0.0020963338165057,
  0.002096333816505706,
  0.002096333816505719,
  0.002217064368779988,
  0.002217064368780136,
  0.002217064368780653,
  0.002614843457608431,
  0.0026148434576086,
  0.002614843457608743,
  0.002816358486732715,
  0.002816358486732837,
  0.002816358486733098,
  0.002835998912930563,
  0.002835998912930566,
  0.002835998912930758,
  0.003126730725424427,
  0.003126730725424463,
  0.003126730725424529,
  0.003153973602536165,
  0.003153973602536455,
  0.00315397360253695,
  0.003163187183116422,
  0.003163187183116666,
  0.003163187183116705,
  0.003221580435286838,
  0.003221580435287081,
  0.00322158043528719,
  0.003339627167696848,
  0.003339627167697182,
  0.003339627167697222,
  0.00367774167811276,
  0.003677741678112901,
  0.003677741678112909,
  0.004205214423890247,
  0.004205214423890422,
  0.004205214423891097,
  0.004942955441682392,
  0.005332292154378799,
  0.005332292154379329,
  0.005332292154379453,
  0.006299077114277314,
  0.006299077114277537,
  0.006299077114277775,
  0.00737803689793278,
  0.007378036897933093,
  0.007378036897933695,
  0.00771631583170163,
  0.007716315831701642,
  0.007716315831701708,
  0.007807035967871289,
  0.007807035967872181,
  0.007807035967872265,
  0.007846508554369643,
  0.007846508554370055,
  0.007846508554370087,
  0.008000596024054854,
  0.00800059602405496,
  0.008000596024054986,
  0.008315808353509287,
  0.008315808353509403,
  0.008315808353509861,
  0.008418522805063788,
  0.008418522805064077,
  0.008418522805064284,
  0.00858375505374044,
  0.008583755053740592,
  0.008583755053740759,
  0.008688757350711517,
  0.008688757350712022,
  0.008688757350712244,
  0.00912078610871582,
  0.00912078610871593,
  0.009120786108716009,
  0.01110598507329943,
  0.01113988077259748,
  0.01113988077259774,
  0.01113988077259806,
  0.01145960029416907,
  0.0114596002941693,
  0.01145960029416939,
  0.01155178034448177,
  0.01155178034448203,
  0.01155178034448213,
  0.01170383356047521,
  0.01170383356047528,
  0.01170383356047564,
  0.011887985191612,
  0.01188798519161229,
  0.01188798519161249,
  0.01215673761841356,
  0.0121567376184137,
  0.01215673761841393,
  0.01313945192856208,
  0.01313945192856243,
  0.01313945192856289,
  0.01552667874066526,
  0.01552667874066688,
  0.01552667874066833,
  0.01690847088733956,
  0.01690847088734039,
  0.01690847088734145,
  0.01878337843692898,
  0.01878337843692938,
  0.01878337843692946,
  0.01950856083079681,
  0.01950856083079749,
  0.01950856083079761,
  0.02195224112844436,
  0.02195224112844458,
  0.02195224112844476,
  0.02551715280129824,
  0.02950496737799784,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
namespace {
const double tetrahedronRule13Points[] = {
  0.01034510725658796, 0.01034510725652366, 0.9689646782302881, 0.01034510725660032,
  0.9412811493523093, 0.008913012362466612, 0.03023687451099998, 0.01956896377422408,
  0.008913012362483565, 0.01956896377423934, 0.03023687451100695, 0.9412811493522701,
  0.01956896377427091, 0.9412811493522358, 0.03023687451100657, 0.008913012362486726,
  0.008603145262962948, 0.8844920682248393, 0.02544900390361993, 0.08145578260857789,
  0.08145578260860413, 0.008603145262975986, 0.02544900390362636, 0.8844920682247935,
  0.8844920682247885, 0.08145578260858234, 0.02544900390363992, 0.0086031452629892,
  0.07915594917543556, 0.87881874683591, 0.008412158658388869, 0.03361314533026558,
  0.03361314533024481, 0.07915594917539193, 0.008412158658414975, 0.8788187468359483,
  0.8788187468359566, 0.03361314533023658, 0.008412158658423473, 0.07915594917538334,
  0.02072452926120901, 0.2820938675417852, 0.005896688536536578, 0.6912849146604692,
  0.6912849146605238, 0.02072452926121111, 0.005896688536550856, 0.2820938675417143,
  0.282093867541703, 0.691284914660533, 0.005896688536556295, 0.02072452926120764,
  0.660612504418027, 0.00423850950551799, 0.3059064193536999, 0.0292425667227551,
  0.004238509505525088, 0.02924256672275331, 0.305906419353717, 0.6606125044180047,
  0.02924256672275465, 0.660612504417956, 0.3059064193537546, 0.004238509505534782,
  0.8108726651448125, 0.03145181004767937, 0.1465204590611696, 0.01115506574633854,
  0.01115506574634481, 0.8108726651448392, 0.1465204590611652, 0.03145181004765069,
  0.03145181004765925, 0.01115506574634996, 0.1465204590611479, 0.8108726651448429,
  0.01337142894352578, 0.0611452791183259, 0.1074571297438097, 0.8180261621943387,
  0.06114527911829663, 0.8180261621942968, 0.1074571297438493, 0.01337142894355733,
  0.8180261621944124, 0.01337142894356406, 0.1074571297437935, 0.06114527911823001,
  0.007414460977235957, 0.6955288748491347, 0.02821381240546334, 0.268842851768166,
  0.6955288748491215, 0.268842851768176, 0.02821381240546195, 0.007414460977240522,
  0.2688428517681751, 0.007414460977257575, 0.02821381240545042, 0.6955288748491169,
  0.02477429690597821, 0.007482222177392445, 0.5213287809539923, 0.4464146999626371,
  0.007482222177401224, 0.4464146999625711, 0.5213287809540651, 0.02477429690596256,
  0.4464146999626367, 0.02477429690598193, 0.5213287809539731, 0.007482222177408238,
  0.02112965969938043, 0.09035183340349828, 0.86581765678534, 0.02270085011178136,
  0.09035183340359541, 0.02270085011179018, 0.8658176567852218, 0.02112965969939262,
  0.02270085011179335, 0.0211296596993924, 0.8658176567851917, 0.09035183340362252,
  0.3417930742320212, 0.002594165265187326, 0.5797685345851115, 0.07584422591768003,
  0.002594165265210041, 0.07584422591768267, 0.5797685345850755, 0.3417930742320318,
  0.07584422591769545, 0.3417930742320845, 0.579768534585002, 0.002594165265218051,
  0.4847746571587412, 0.4810641377028125, 0.01833057078756236, 0.01583063435088392,
  0.4810641377027924, 0.01583063435090152, 0.01833057078755179, 0.4847746571587543,
  0.0158306343508983, 0.4847746571587827, 0.01833057078756206, 0.481064137702757,
  0.1676137196659997, 0.7086431089234964, 0.002914466641356441, 0.1208287047691475,
  0.7086431089235703, 0.1208287047691087, 0.002914466641385641, 0.1676137196659353,
  0.1208287047691088, 0.1676137196659543, 0.002914466641410491, 0.7086431089235264,
  0.05182981415363299, 0.7671835222425682, 0.01275903790005842, 0.1682276257037404,
  0.767183522242537, 0.1682276257037641, 0.01275903790006475, 0.05182981415363405,
  0.1682276257037143, 0.05182981415365493, 0.01275903790008807, 0.7671835222425427,
  0.1603808640957398, 0.780025722472745, 0.04144316733981209, 0.01815024609170305,
  0.01815024609171124, 0.1603808640958211, 0.04144316733977616, 0.7800257224726914,
  0.7800257224727031, 0.0181502460917103, 0.04144316733980475, 0.1603808640957819,
  0.001030437977338548, 0.3006497694477112, 0.5608693977782155, 0.1374503947967347,
  0.3006497694476872, 0.1374503947967453, 0.560869397778206, 0.001030437977361576,
  0.1374503947967274, 0.00103043797737723, 0.5608693977782493, 0.3006497694476461,
  0.009571364698298758, 0.6068954673005267, 0.3058952472331785, 0.07763792076799608,
  0.6068954673005383, 0.07763792076797839, 0.3058952472331658, 0.009571364698317486,
  0.07763792076798627, 0.009571364698318083, 0.3058952472331321, 0.6068954673005635,
  0.2359081252750476, 0.02712491103418074, 0.7148030256628792, 0.0221639380278924,
  0.02712491103418163, 0.02216393802789915, 0.7148030256628535, 0.2359081252750658,
  0.02216393802790523, 0.2359081252749586, 0.7148030256629532, 0.02712491103418291,
  0.5611854641624137, 0.3497758718670665, 0.01001327495242358, 0.07902538901809628,
  0.07902538901810821, 0.5611854641624555, 0.01001327495242865, 0.3497758718670076,
  0.3497758718669661, 0.0790253890181477, 0.01001327495243759, 0.5611854641624486,
  0.01201591051800159, 0.7035601418166272, 0.1282324135027442, 0.156191534162627,
  0.1561915341626666, 0.01201591051801169, 0.1282324135027487, 0.7035601418165731,
  0.7035601418165589, 0.1561915341626685, 0.1282324135027578, 0.01201591051801476,
  0.01227254816726416, 0.1520983651999485, 0.1736456691583085, 0.6619834174744789,
  0.1520983651998947, 0.6619834174744651, 0.1736456691583576, 0.01227254816728268,
  0.6619834174745407, 0.01227254816727948, 0.1736456691582867, 0.1520983651998931,
  0.009608952348337692, 0.5009662598450281, 0.2173473462639225, 0.2720774415427117,
  0.5009662598449669, 0.2720774415427657, 0.21734734626392, 0.009608952348347438,
  0.2720774415427986, 0.009608952348355002, 0.2173473462639029, 0.5009662598449434,
  0.117142028395487, 0.1306252415276769, 0.7370755718293556, 0.01515715824748054,
  0.01515715824748938, 0.1171420283955028, 0.7370755718293308, 0.130625241527677,
  0.1306252415276693, 0.01515715824751321, 0.7370755718293365, 0.117142028395481,
  0.06596911170718446, 0.4869178929175357, 0.4164421277991943, 0.03067086757608556,
  0.03067086757606238, 0.06596911170715442, 0.4164421277993404, 0.4869178929174427,
  0.4869178929174335, 0.03067086757608414, 0.4164421277992895, 0.06596911170719272,
  0.06180743725428443, 0.7796220928971531, 0.07217289794213186, 0.08639757190643063,
  0.08639757190638243, 0.06180743725431112, 0.07217289794220663, 0.7796220928970998,
  0.7796220928970106, 0.08639757190646453, 0.07217289794218502, 0.06180743725433989,
  0.2124417592665611, 0.3704425559581763, 0.01068152306355014, 0.4064341617117125,
  0.4064341617117311, 0.2124417592666155, 0.01068152306356992, 0.3704425559580835,
  0.3704425559580568, 0.4064341617118274, 0.01068152306357016, 0.2124417592665457,
  0.01757754194097423, 0.3170690280570044, 0.0808011880664319, 0.5845522419355894,
  0.3170690280569446, 0.5845522419356186, 0.08080118806646398, 0.01757754194097282,
  0.584552241935574, 0.017577541940982, 0.0808011880664406, 0.3170690280570034,
  0.4819714524309398, 0.01756230923632635, 0.3414320148667813, 0.1590342234659526,
  0.1590342234659364, 0.4819714524309074, 0.3414320148668196, 0.01756230923633656,
  0.01756230923633349, 0.1590342234659289, 0.3414320148668064, 0.4819714524309313,
  0.08902566699068729, 0.3386042162630997, 0.02525485039503888, 0.5471152663511741,
  0.3386042162631206, 0.5471152663511726, 0.02525485039504986, 0.08902566699065692,
  0.5471152663511358, 0.08902566699071175, 0.02525485039503578, 0.3386042162631167,
  0.05285544098330982, 0.4000979296301265, 0.4641321089536249, 0.08291452043293879,
  0.4000979296298913, 0.0829145204330444, 0.4641321089536999, 0.05285544098336448,
  0.08291452043303993, 0.05285544098335554, 0.4641321089535966, 0.400097929630008,
  0.01782606090077854, 0.2874706358928882, 0.3856172937149586, 0.3090860094913746,
  0.2874706358928806, 0.3090860094913717, 0.3856172937149701, 0.01782606090077765,
  0.3090860094913699, 0.01782606090078187, 0.3856172937149664, 0.2874706358928818,
  0.3710934105995327, 0.02657234084597485, 0.09690187156313018, 0.5054323769913622,
  0.02657234084597537, 0.5054323769913355, 0.09690187156315631, 0.3710934105995328,
  0.5054323769913123, 0.371093410599567, 0.09690187156314264, 0.02657234084597807,
  0.02148831270206694, 0.3206072988650484, 0.2127349091997354, 0.4451694792331493,
  0.4451694792332048, 0.02148831270207087, 0.2127349091997207, 0.3206072988650036,
  0.3206072988650124, 0.445169479233177, 0.2127349091997361, 0.02148831270207452,
  0.0951170007288927, 0.0951170007290063, 0.7146489978132146, 0.0951170007288864,
  0.1735802358450919, 0.02890436352483536, 0.3570824842180014, 0.4404329164120713,
  0.4404329164120814, 0.1735802358450641, 0.3570824842179925, 0.02890436352486198,
  0.02890436352488776, 0.4404329164119998, 0.357082484218023, 0.1735802358450894,
  0.08023850116226482, 0.6174866483249893, 0.07195784522707145, 0.2303170052856744,
  0.6174866483249148, 0.2303170052857254, 0.0719578452270639, 0.0802385011622959,
  0.2303170052856326, 0.08023850116232735, 0.07195784522713053, 0.6174866483249095,
  0.09452881219751588, 0.1751776752009559, 0.07065601264629488, 0.6596374999552334,
  0.1751776752009207, 0.6596374999553175, 0.07065601264621812, 0.09452881219754372,
  0.6596374999552117, 0.09452881219755312, 0.0706560126462567, 0.1751776752009785,
  0.06541766890798655, 0.0754347492130809, 0.2206728628957595, 0.6384747189831731,
  0.6384747189831496, 0.0654176689080234, 0.2206728628957641, 0.0754347492130629,
  0.07543474921303878, 0.6384747189831916, 0.22067286289572, 0.06541766890804965,
  0.5321359768315169, 0.2362423058619533, 0.03066111663210869, 0.2009606006744211,
  0.2362423058618978, 0.2009606006744852, 0.03066111663211837, 0.5321359768314987,
  0.200960600674406, 0.5321359768315502, 0.03066111663213887, 0.2362423058619049,
  0.2434135622407882, 0.1003198536332518, 0.5906059332310526, 0.06566065089490747,
  0.1003198536332653, 0.06566065089495007, 0.5906059332310177, 0.2434135622407669,
  0.06566065089490132, 0.2434135622409514, 0.590605933230827, 0.1003198536333202,
  0.03545951407500253, 0.1645691312152424, 0.5385515468421933, 0.2614198078675618,
  0.2614198078675792, 0.03545951407500569, 0.5385515468421994, 0.1645691312152157,
  0.1645691312152262, 0.2614198078675275, 0.5385515468422312, 0.03545951407501513,
  0.078850996951403, 0.2214791068336956, 0.1663421652944799, 0.5333277309204216,
  0.5333277309204181, 0.07885099695144153, 0.1663421652944797, 0.2214791068336607,
  0.2214791068336244, 0.533327730920471, 0.1663421652944595, 0.0788509969514451,
  0.0773186488433034, 0.5438135338904002, 0.1960861755130517, 0.1827816417532447,
  0.1827816417531721, 0.0773186488433082, 0.1960861755131724, 0.5438135338903474,
  0.5438135338903273, 0.1827816417532548, 0.1960861755130822, 0.07731864884333575,
  0.1668632870416709, 0.1668632870415595, 0.4994101388751889, 0.1668632870415807,
  0.1227490628669584, 0.3909296074394038, 0.08756388655247146, 0.3987574431411663,
  0.3987574431411315, 0.1227490628669686, 0.0875638865525005, 0.3909296074393993,
  0.3909296074393537, 0.3987574431411711, 0.08756388655250151, 0.1227490628669736,
  0.276668775818374, 0.2188997970179869, 0.4020005482407241, 0.102430878922915,
  0.2188997970179731, 0.1024308789229114, 0.4020005482406983, 0.2766687758184172,
  0.1024308789229648, 0.2766687758182949, 0.4020005482407235, 0.2188997970180168,
  0.3095550183430513, 0.3095550183430962, 0.07133494497075156, 0.309555018343101,
  0.3138415213429039, 0.09663461813535858, 0.2305808594445332, 0.3589430010772042,
  0.3589430010771437, 0.3138415213429264, 0.230580859444564, 0.09663461813536586,
  0.09663461813536428, 0.3589430010771935, 0.2305808594445379, 0.3138415213429043,
  0.4418055888803888, 0.2069223626302676, 0.1404348940839113, 0.2108371544054322,
  0.210837154405392, 0.4418055888803925, 0.1404348940839597, 0.2069223626302559,
  0.206922362630213, 0.2108371544054255, 0.1404348940839574, 0.4418055888804041,
  0.1108495022995848, 0.1626179922026075, 0.3263197105354871, 0.4002127949623205,
  0.4002127949623002, 0.1108495022995989, 0.3263197105354845, 0.1626179922026164,
  0.1626179922025704, 0.4002127949623043, 0.326319710535522, 0.1108495022996032,
  0.2505588869395824, 0.2505588869395491, 0.2483233391813068, 0.2505588869395617,
};
const double tetrahedronRule13Weights[] = {
  0.0002480594675168803,
  0.000650491962223052,
  0.000650491962224175,
  0.0006504919622251082,
  0.001290974956953882,
  0.001290974956955246,
  0.001290974956956647,
  0.001340851547869289,
  0.001340851547870439,
  0.001340851547871066,
  0.001431208149429356,
  0.001431208149430814,
  0.001431208149431119,
  0.002016789985488527,
  0.00201678998548882,
  0.002016789985490143,
  0.002088390612147266,
  0.002088390612147368,
  0.002088390612148554,
  0.002130735544378634,
  0.00213073554438061,
  0.002130735544381179,
  0.002136503704822046,
  0.002136503704822481,
  0.002136503704823818,
  0.002214867394998551,
  0.0022148673949988,
  0.002214867395000742,
  0.00222704248813359,
  0.002227042488135406,
  0.002227042488135766,
  0.002412787372148824,
  0.002412787372151328,
  0.002412787372153638,
  0.002492611378149027,
  0.002492611378150218,
  0.002492611378150285,
  0.002560191587547936,
  0.002560191587551527,
  0.00256019158755455,
  0.002718142703234164,
  0.002718142703234617,
  0.002718142703237677,
  0.003110144144971738,
  0.003110144144971966,
  0.003110144144972429,
  0.003205036237160009,
  0.003205036237163785,
  0.003205036237166612,
  0.00393054515240341,
  0.003930545152406018,
  0.003930545152406475,
  0.003971541178919466,
  0.003971541178920297,
  0.003971541178922642,
  0.004142773176415053,
  0.004142773176415798,
  0.004142773176419249,
  0.004510424642995273,
  0.004510424642999121,
  0.004510424642999344,
  0.004638629681744651,
  0.004638629681748835,
  0.00463862968174892,
  0.004760728826715785,
  0.004760728826718033,
  0.004760728826718926,
  0.004801572278215449,
  0.00480157227821793,
  0.004801572278222341,
  0.004886855150821356,
  0.004886855150822266,
  0.004886855150829719,
  0.005527674674459776,
  0.00552767467446142,
  0.005527674674463838,
  0.005590238647201325,
  0.005590238647206236,
  0.005590238647206961,
  0.005632805402396634,
  0.005632805402396995,
  0.005632805402398852,
  0.006766622541764133,
  0.00676662254176657,
  0.006766622541766761,
  0.006935147143899732,
  0.006935147143900422,
  0.006935147143901512,
  0.007067246329643165,
  0.007067246329654151,
  0.007067246329660336,
  0.007583310463113181,
  0.007583310463114,
  0.007583310463114458,
  0.00785916073165506,
  0.00785916073165542,
  0.007859160731656363,
  0.00829497134333823,
  0.008294971343338606,
  0.008294971343339612,
  0.008631390479076347,
  0.009141350634070546,
  0.009141350634079419,
  0.009141350634087499,
  0.009320328536744166,
  0.009320328536746404,
  0.009320328536752947,
  0.009471371720718021,
  0.009471371720719352,
  0.009471371720719423,
  0.009658673209736351,
  0.009658673209738493,
  0.009658673209738526,
  0.01008129683578955,
  0.01008129683579076,
  0.01008129683579227,
  0.01065871747742306,
  0.01065871747743018,
  0.01065871747743694,
  0.01085243167679074,
  0.010852431676792,
  0.01085243167679318,
  0.01146275018831309,
  0.01146275018831698,
  0.01146275018832084,
  0.01276467994129703,
  0.01276467994129944,
  0.01276467994130476,
  0.01404013668370559,
  0.0153606971274897,
  0.015360697127492,
  0.01536069712749215,
  0.01542681751246374,
  0.01542681751246688,
  0.01542681751246816,
  0.01700568262347133,
  0.01777013133272348,
  0.01777013133272481,
  0.01777013133272617,
  0.01870056597068023,
  0.01870056597068039,
  0.01870056597068342,
  0.01982019940924874,
  0.01982019940925496,
  0.01982019940925693,
  0.02582364461938367,
};
const double tetrahedronRule14Points[] = {
  0.006857703680959708, 0.006857703681460325, 0.9794268889578419, 0.006857703679738036,
  0.009252353846064727, 0.004788844763930928, 0.03329961033004269, 0.9526591910599617,
  0.9526591910590293, 0.009252353846425697, 0.03329961033024104, 0.004788844764303968,
  0.004788844764298505, 0.9526591910584257, 0.03329961033063356, 0.00925235384664224,
  0.06141444425249755, 0.9232999651585443, 0.002010058648387674, 0.0132755319405705,
  0.9232999651574737, 0.01327553194083024, 0.002010058649115951, 0.06141444425258011,
  0.01327553194070744, 0.06141444425278526, 0.002010058649810132, 0.9232999651566971,
  0.01773414386230762, 0.8989650605386635, 0.01446762164021698, 0.06883317395881183,
  0.8989650605385748, 0.0688331739588598, 0.01446762164046387, 0.0177341438621015,
  0.06883317395833545, 0.01773414386215409, 0.01446762164064887, 0.8989650605388616,
  0.009247363617832223, 0.3990139062271814, 0.5829037436121112, 0.008834986542875178,
  0.399013906225403, 0.008834986543019535, 0.5829037436136701, 0.009247363617907345,
  0.008834986543086735, 0.009247363618203858, 0.5829037436168685, 0.3990139062218409,
  0.7709900229262808, 0.01952291262766601, 0.01015620879258834, 0.1993308556534648,
  0.01952291262769855, 0.1993308556536677, 0.01015620879265931, 0.7709900229259744,
  0.1993308556534236, 0.7709900229262199, 0.01015620879270446, 0.01952291262765199,
  0.02032554506145879, 0.7220074978401071, 0.2431115808353706, 0.0145553762630635,
  0.7220074978408385, 0.01455537626308008, 0.2431115808345355, 0.02032554506154596,
  0.01455537626344418, 0.02032554506140792, 0.2431115808356294, 0.7220074978395185,
  0.01883099256369943, 0.01956534940768639, 0.8819163274688043, 0.07968733055980981,
  0.07968733056157902, 0.01883099256402238, 0.8819163274665061, 0.01956534940789245,
  0.01956534940798839, 0.07968733056254174, 0.8819163274654277, 0.01883099256404219,
  0.8343838905775879, 0.02228963644433849, 0.1242803391217787, 0.01904613385629492,
  0.02228963644438797, 0.0190461338562963, 0.1242803391208842, 0.8343838905784315,
  0.01904613385630611, 0.8343838905759399, 0.1242803391233692, 0.02228963644438475,
  0.2039231912002361, 0.02012121561803056, 0.01440053742030228, 0.7615550557614311,
  0.02012121561804498, 0.7615550557610796, 0.01440053742029756, 0.2039231912005778,
  0.7615550557609511, 0.2039231912006661, 0.01440053742036038, 0.02012121561802244,
  0.3361509636180879, 0.384645703604847, 0.2764557088059904, 0.002747623971074753,
  0.002747623971354991, 0.3361509636165141, 0.2764557088037994, 0.3846457036083315,
  0.3846457036073966, 0.002747623971615903, 0.276455708804184, 0.3361509636168036,
  0.350859996445968, 0.5522182104345288, 0.004931325226067042, 0.09199046789343618,
  0.5522182104342734, 0.09199046789365573, 0.004931325226427101, 0.3508599964456438,
  0.09199046789304373, 0.3508599964450814, 0.004931325226952402, 0.5522182104349225,
  0.02152082553450803, 0.0160803500126914, 0.379120808464382, 0.5832780159884186,
  0.5832780159922265, 0.02152082553456097, 0.3791208084604637, 0.01608035001274882,
  0.01608035001313742, 0.5832780159937186, 0.379120808458791, 0.02152082553435292,
  0.00323980932956962, 0.08400887661431675, 0.386296150270937, 0.5264551637851766,
  0.5264551637848466, 0.003239809329937143, 0.3862961502712207, 0.08400887661399553,
  0.0840088766149807, 0.5264551637842712, 0.3862961502705597, 0.00323980933018847,
  0.09120718428587543, 0.00411013141124883, 0.3989904928634934, 0.5056921914393824,
  0.004110131411517128, 0.5056921914391684, 0.3989904928650359, 0.09120718428427849,
  0.5056921914383363, 0.09120718428557456, 0.3989904928644713, 0.004110131411617812,
  0.5156439635468597, 0.2349406124884029, 0.2474912783867316, 0.001924145578005798,
  0.2349406124899761, 0.001924145578256931, 0.2474912783858402, 0.5156439635459269,
  0.001924145578230063, 0.5156439635453917, 0.2474912783874761, 0.2349406124889022,
  0.01932237274818349, 0.07638832520527908, 0.05638385444735509, 0.8479054475991824,
  0.8479054475994247, 0.01932237274817627, 0.05638385444701339, 0.07638832520538569,
  0.07638832520496093, 0.8479054476003125, 0.05638385444661988, 0.01932237274810664,
  0.3823009464917305, 0.0167988939596847, 0.02255542412116617, 0.5783447354274186,
  0.01679889395970684, 0.5783447354272748, 0.02255542412126642, 0.3823009464917519,
  0.5783447354271684, 0.3823009464918677, 0.02255542412122661, 0.01679889395973734,
  0.2129425371446761, 0.0212807476383709, 0.7437074210582457, 0.02206929415870729,
  0.02206929415866949, 0.2129425371459558, 0.7437074210569653, 0.02128074763840937,
  0.02128074763856252, 0.02206929415888909, 0.7437074210601419, 0.2129425371424064,
  0.3317239526150014, 0.3317239526139896, 0.004828142155987282, 0.3317239526150217,
  0.5404797680657268, 0.007294355381304199, 0.2453763152229318, 0.2068495613300372,
  0.007294355381551722, 0.2068495613301014, 0.2453763152216877, 0.5404797680666592,
  0.2068495613312503, 0.5404797680654154, 0.2453763152219601, 0.007294355381374185,
  0.8058111958219785, 0.09857704079908997, 0.07586181203272872, 0.01974995134620285,
  0.01974995134613911, 0.8058111958226273, 0.07586181203231102, 0.0985770407989226,
  0.09857704079958525, 0.0197499513461522, 0.07586181203295679, 0.8058111958213057,
  0.01748287896089844, 0.3792756315222444, 0.02304572711563008, 0.580195762401227,
  0.3792756315220148, 0.5801957624014105, 0.02304572711563284, 0.01748287896094188,
  0.5801957624013359, 0.01748287896096796, 0.02304572711565241, 0.3792756315220438,
  0.2874224758303754, 0.005601417694663574, 0.6029413319659248, 0.1040347745090362,
  0.1040347745094613, 0.2874224758296852, 0.6029413319661477, 0.00560141769470579,
  0.005601417694883342, 0.104034774509157, 0.6029413319657438, 0.2874224758302159,
  0.1114551583386971, 0.01030235261682538, 0.7627564092743483, 0.1154860797701293,
  0.01030235261707004, 0.1154860797700707, 0.7627564092740204, 0.1114551583388388,
  0.1154860797697298, 0.1114551583385124, 0.7627564092743049, 0.01030235261745294,
  0.2935488505770338, 0.09761999738538321, 0.6006213514676992, 0.00820980056988374,
  0.09761999738502115, 0.008209800569967951, 0.6006213514669282, 0.2935488505780827,
  0.008209800569969635, 0.293548850577753, 0.6006213514668876, 0.09761999738538973,
  0.08497804426593077, 0.517513525717932, 0.01294633315160566, 0.3845620968645316,
  0.5175135257172315, 0.3845620968650357, 0.01294633315184834, 0.0849780442658844,
  0.3845620968647721, 0.08497804426566612, 0.01294633315189131, 0.5175135257176705,
  0.7877678986243767, 0.09409500064304101, 0.01931078849337184, 0.09882631223921047,
  0.09882631223971038, 0.7877678986241535, 0.01931078849337398, 0.0940950006427621,
  0.09409500064289474, 0.09882631223940282, 0.0193107884933751, 0.7877678986243273,
  0.5497595632204098, 0.01252905980804105, 0.1219406461222866, 0.3157707308492627,
  0.01252905980810353, 0.3157707308500686, 0.1219406461215593, 0.5497595632202685,
  0.3157707308512963, 0.5497595632185667, 0.1219406461220274, 0.0125290598081097,
  0.5303977839664743, 0.2336768622507286, 0.008568966905135528, 0.2273563868776616,
  0.2273563868775282, 0.5303977839660673, 0.008568966905105817, 0.2336768622512988,
  0.2336768622504743, 0.2273563868768414, 0.008568966905196002, 0.5303977839674883,
  0.01341116464697127, 0.6612982036782233, 0.09601282934079287, 0.2292778023340126,
  0.2292778023349974, 0.01341116464707565, 0.0960128293404185, 0.6612982036775084,
  0.661298203678323, 0.2292778023338679, 0.09601282934065727, 0.01341116464715178,
  0.6533880188663116, 0.2247326755186619, 0.01699262706566816, 0.1048866785493583,
  0.10488667854954, 0.6533880188669758, 0.01699262706582885, 0.2247326755176553,
  0.2247326755185866, 0.1048866785488491, 0.01699262706599834, 0.6533880188665658,
  0.2612596694959481, 0.007667507939535023, 0.4304413398190844, 0.3006314827454324,
  0.3006314827447682, 0.2612596694952175, 0.430441339820285, 0.007667507939729312,
  0.007667507939682639, 0.3006314827445465, 0.4304413398197249, 0.261259669496046,
  0.01940675068598702, 0.1990033699311775, 0.07543662479224182, 0.7061532545905936,
  0.7061532545902, 0.01940675068596605, 0.07543662479225494, 0.1990033699315791,
  0.1990033699315986, 0.706153254589724, 0.07543662479267595, 0.01940675068600144,
  0.2153693225142795, 0.07162380480079734, 0.0661407842999457, 0.6468660883849775,
  0.07162380480015625, 0.6468660883848494, 0.06614078429932518, 0.2153693225156691,
  0.6468660883845436, 0.2153693225150791, 0.06614078429928018, 0.07162380480109713,
  0.077815923168826, 0.07781592316817382, 0.7665522304918784, 0.07781592317112174,
  0.01877419874737987, 0.1014405096223781, 0.1843049531492825, 0.6954803384809596,
  0.6954803384805778, 0.01877419874750536, 0.1843049531493682, 0.1014405096225487,
  0.1014405096223557, 0.6954803384805676, 0.1843049531495559, 0.01877419874752084,
  0.09578855271960066, 0.01823203771678103, 0.2102844818945803, 0.675694927669038,
  0.6756949276694415, 0.09578855271908891, 0.2102844818946296, 0.01823203771683995,
  0.01823203771688221, 0.6756949276687967, 0.2102844818947134, 0.09578855271960776,
  0.4739258549152569, 0.394299156898155, 0.1145335941286789, 0.01724139405790906,
  0.394299156900111, 0.01724139405791831, 0.1145335941285089, 0.4739258549134616,
  0.01724139405793893, 0.4739258549146191, 0.1145335941289155, 0.3942991568985264,
  0.09983516167455454, 0.2235331462354234, 0.02642159417479953, 0.6502100979152226,
  0.6502100979152713, 0.09983516167429868, 0.02642159417490681, 0.2235331462355232,
  0.2235331462366786, 0.650210097913948, 0.026421594174992, 0.09983516167438135,
  0.04604965750902205, 0.3968682475417654, 0.5163227682090831, 0.0407593267401295,
  0.3968682475411293, 0.0407593267406208, 0.5163227682092674, 0.04604965750898249,
  0.04075932674082398, 0.04604965750936901, 0.5163227682088478, 0.3968682475409593,
  0.5706340243899409, 0.08400311872986549, 0.105036530907377, 0.2403263259728166,
  0.240326325971861, 0.5706340243897189, 0.1050365309082531, 0.08400311873016701,
  0.08400311873016891, 0.240326325974372, 0.1050365309055699, 0.5706340243898892,
  0.1932367143291832, 0.0713650912511827, 0.6582528796899906, 0.07714531472964359,
  0.07714531472941318, 0.1932367143282536, 0.6582528796907257, 0.0713650912516075,
  0.07136509125209903, 0.07714531472977029, 0.658252879686536, 0.1932367143315947,
  0.07837424052530441, 0.3761818136931925, 0.07236155120489983, 0.4730823945766033,
  0.4730823945784287, 0.07837424052573189, 0.07236155120465555, 0.3761818136911839,
  0.3761818136912941, 0.473082394578608, 0.07236155120451863, 0.0783742405255793,
  0.08923568468861766, 0.5115423865329087, 0.09281715399980724, 0.3064047747786664,
  0.3064047747789605, 0.08923568468759871, 0.09281715400051348, 0.5115423865329274,
  0.5115423865325862, 0.3064047747787268, 0.09281715400041667, 0.08923568468827033,
  0.09737203363634417, 0.1007344014121848, 0.4929088721328376, 0.3089846928186334,
  0.3089846928173871, 0.09737203363532915, 0.492908872135997, 0.1007344014112866,
  0.1007344014106231, 0.3089846928177313, 0.4929088721369547, 0.09737203363469077,
  0.1775478833143351, 0.3899676091564037, 0.4030241508000952, 0.02946035672916597,
  0.3899676091567567, 0.02946035672918423, 0.4030241508003236, 0.1775478833137354,
  0.02946035672919241, 0.1775478833136099, 0.403024150799614, 0.3899676091575836,
  0.0382221895291049, 0.2034004094915035, 0.5628552072214578, 0.1955221937579338,
  0.195522193757886, 0.03822218952882864, 0.5628552072215468, 0.2034004094917387,
  0.2034004094916, 0.1955221937576974, 0.5628552072214532, 0.03822218952924938,
  0.391993350183357, 0.1914181781007838, 0.03060828252772313, 0.385980189188136,
  0.3859801891875482, 0.3919933501838906, 0.03060828252764542, 0.1914181781009157,
  0.1914181781009923, 0.3859801891869217, 0.03060828252764046, 0.3919933501844455,
  0.03830546710979171, 0.4143211516037891, 0.3863688156730401, 0.161004565613379,
  0.4143211516027137, 0.1610045656138734, 0.3863688156733209, 0.03830546711009203,
  0.1610045656134992, 0.0383054671100454, 0.3863688156731704, 0.414321151603285,
  0.2056632530541998, 0.05411126130896651, 0.2061145172704723, 0.5341109683663615,
  0.5341109683662314, 0.2056632530540627, 0.2061145172707037, 0.05411126130900221,
  0.05411126130928814, 0.5341109683657477, 0.2061145172697658, 0.2056632530551984,
  0.1015171591699777, 0.1020634349618442, 0.1162724881045504, 0.6801469177636278,
  0.6801469177635077, 0.1015171591702443, 0.1162724881044248, 0.1020634349618232,
  0.102063434961655, 0.6801469177636642, 0.1162724881042698, 0.101517159170411,
  0.06794709903225467, 0.08050368241686043, 0.3036135923650056, 0.5479356261858792,
  0.5479356261852021, 0.0679470990326355, 0.3036135923649413, 0.08050368241722111,
  0.08050368241747642, 0.5479356261849525, 0.3036135923645354, 0.0679470990330357,
  0.2160065443462191, 0.5071777807646763, 0.2145116281103287, 0.06230404677877585,
  0.5071777807651786, 0.06230404677880914, 0.2145116281099157, 0.2160065443460965,
  0.06230404677908077, 0.2160065443456221, 0.2145116281088852, 0.5071777807664121,
  0.1271466762690916, 0.167752470283245, 0.3465563262838002, 0.3585445271638631,
  0.1677524702817992, 0.358544527163581, 0.3465563262852937, 0.1271466762693261,
  0.3585445271645286, 0.1271466762697583, 0.3465563262840383, 0.1677524702816747,
  0.3502614515179938, 0.04637577761701088, 0.2412387153575752, 0.3621240555074202,
  0.3621240555078011, 0.3502614515181501, 0.2412387153574093, 0.04637577761663944,
  0.04637577761704335, 0.3621240555066351, 0.2412387153578485, 0.3502614515184731,
  0.5035445472625852, 0.2096968537717866, 0.07908151868224303, 0.2076770802833851,
  0.2076770802830252, 0.5035445472625711, 0.07908151868236299, 0.2096968537720406,
  0.2096968537719228, 0.207677080282593, 0.07908151868295447, 0.5035445472625297,
  0.09704125425919986, 0.2851510675157584, 0.3639850895836558, 0.2538225886413859,
  0.2851510675153835, 0.2538225886425896, 0.363985089582452, 0.097041254259575,
  0.2538225886423787, 0.09704125425935214, 0.3639850895833628, 0.2851510675149063,
  0.3029181193293014, 0.3029181193293765, 0.09124564201234239, 0.3029181193289797,
  0.4526488719953613, 0.1783434906135457, 0.2141553642703896, 0.1548522731207034,
  0.1783434906131041, 0.1548522731197198, 0.2141553642717896, 0.4526488719953865,
  0.1548522731205867, 0.4526488719948076, 0.2141553642709648, 0.1783434906136407,
  0.165887520255092, 0.165887520255045, 0.5023374392351683, 0.1658875202546948,
  0.1538060360803229, 0.3322960833854866, 0.1644327097770143, 0.3494651707571762,
  0.332296083385749, 0.3494651707568161, 0.1644327097772045, 0.1538060360802305,
  0.3494651707565804, 0.1538060360803426, 0.1644327097771141, 0.332296083385963,
  0.2432210319415151, 0.2432210319416702, 0.2703369041747087, 0.2432210319421061,
};
const double tetrahedronRule14Weights[] = {
  0.0001326304715554318,
  0.0003062422717916081,
  0.0003062422718052223,
  0.0003062422718125822,
  0.0003865523368973635,
  0.0003865523369177293,
  0.0003865523369318582,
  0.0009985509358173324,
  0.0009985509358233183,
  0.0009985509358356878,
  0.00100506631502414,
  0.001005066315035382,
  0.001005066315053699,
  0.001510383294502125,
  0.001510383294509604,
  0.001510383294511446,
  0.001557037123532029,
  0.00155703712356756,
  0.001557037123631163,
  0.001574105140631024,
  0.001574105140670639,
  0.001574105140683729,
  0.001737740804468816,
  0.001737740804472743,
  0.001737740804485786,
  0.001967596134602619,
  0.001967596134602752,
  0.001967596134606619,
  0.002013317271230114,
  0.002013317271272657,
  0.002013317271285124,
  0.002038335190731275,
  0.002038335190790098,
  0.002038335190840345,
  0.002064712890465934,
  0.002064712890473364,
  0.002064712890477832,
  0.002256663233996461,
  0.002256663234040253,
  0.002256663234076034,
  0.002277242268361119,
  0.002277242268384512,
  0.002277242268412218,
  0.002606662555776668,
  0.00260666255582001,
  0.002606662555829621,
  0.002620943094181545,
  0.002620943094204372,
  0.002620943094213716,
  0.002835082464645224,
  0.002835082464658077,
  0.002835082464658189,
  0.002868455103111458,
  0.002868455103117399,
  0.002868455103145995,
  0.002875952853631905,
  0.003030717720368688,
  0.003030717720400125,
  0.003030717720401985,
  0.003071563695482687,
  0.003071563695484445,
  0.003071563695486829,
  0.003080564445580618,
  0.003080564445589803,
  0.003080564445597751,
  0.003095022989361726,
  0.003095022989380672,
  0.003095022989401973,
  0.003143842557385247,
  0.003143842557427992,
  0.003143842557478466,
  0.003464359444750507,
  0.003464359444760797,
  0.003464359444767502,
  0.003474472952247674,
  0.003474472952264732,
  0.003474472952267899,
  0.003624020544269819,
  0.003624020544275046,
  0.003624020544275626,
  0.003683578020296075,
  0.00368357802031626,
  0.00368357802032442,
  0.003802172079287347,
  0.003802172079289692,
  0.003802172079301811,
  0.003809274119446043,
  0.003809274119462113,
  0.003809274119473429,
  0.003871269376928166,
  0.003871269376949657,
  0.003871269376972213,
  0.003949865178581519,
  0.003949865178586763,
  0.003949865178618155,
  0.004081275540612334,
  0.004081275540614281,
  0.004081275540655719,
  0.004320186677478928,
  0.004320186677494429,
  0.00432018667752395,
  0.004759723395406246,
  0.004845932819596691,
  0.004845932819645914,
  0.004845932819659964,
  0.004931010814560586,
  0.004931010814563869,
  0.004931010814602941,
  0.005424409298659606,
  0.005424409298673685,
  0.005424409298691003,
  0.005460989291181884,
  0.005460989291244838,
  0.005460989291290918,
  0.005727261783720176,
  0.005727261783761345,
  0.00572726178378774,
  0.006699651517107228,
  0.006699651517133745,
  0.006699651517141216,
  0.007349501442209064,
  0.0073495014422093,
  0.007349501442246883,
  0.008208997919363397,
  0.008208997919443324,
  0.008208997919495108,
  0.008550551288604278,
  0.008550551288658911,
  0.008550551288677955,
  0.009107867611710199,
  0.009107867611759999,
  0.009107867611766891,
  0.009130619132910684,
  0.009130619132935567,
  0.009130619132941725,
  0.009299955245756457,
  0.009299955245759339,
  0.00929995524576649,
  0.009446739702049126,
  0.009446739702049345,
  0.009446739702065811,
  0.009618158729519025,
  0.009618158729531884,
  0.009618158729557466,
  0.01004340142046944,
  0.0100434014205477,
  0.01004340142055051,
  0.01005857022790992,
  0.01005857022791025,
  0.01005857022791983,
  0.01007559414854637,
  0.01007559414857101,
  0.01007559414858962,
  0.01046629943411991,
  0.01046629943416311,
  0.01046629943418979,
  0.01108962311518957,
  0.0110896231152734,
  0.01108962311529199,
  0.01147674139604568,
  0.01147674139605218,
  0.01147674139609741,
  0.0132295742411817,
  0.01322957424118557,
  0.01322957424125103,
  0.01470178544539434,
  0.01470178544543603,
  0.01470178544547772,
  0.01488953070147238,
  0.01504719421427231,
  0.01504719421427678,
  0.01504719421432172,
  0.01621927038505058,
  0.01790067394810685,
  0.01790067394811538,
  0.01790067394811609,
  0.01906895830895307,
};
const double tetrahedronRule15Points[] = {
  0.02484175292278384, 0.008848046489432548, 0.9372660613009632, 0.02904413928682048,
  0.008848046489437518, 0.02904413928681676, 0.9372660613009608, 0.02484175292278501,
  0.02904413928681213, 0.02484175292278018, 0.9372660613009554, 0.008848046489452255,
  0.003073684779436487, 0.2792517608130759, 0.007826636168369566, 0.7098479182391181,
  0.709847918239126, 0.003073684779447072, 0.007826636168374292, 0.2792517608130526,
  0.2792517608130549, 0.7098479182391227, 0.007826636168374732, 0.003073684779447607,
  0.8851662080559259, 0.01941685525440453, 0.09225347133747239, 0.003163465352197137,
  0.01941685525440571, 0.003163465352201491, 0.09225347133747905, 0.8851662080559137,
  0.003163465352203353, 0.8851662080559214, 0.09225347133747011, 0.01941685525440515,
  0.02062270623222065, 0.9433792085073393, 0.01608597865131358, 0.01991210660912655,
  0.943379208507337, 0.01991210660912664, 0.01608597865131474, 0.0206227062322216,
  0.01991210660912658, 0.02062270623222047, 0.01608597865131562, 0.9433792085073373,
  0.1095755475481473, 0.01464021932495235, 0.8630127527658966, 0.01277148036100373,
  0.01277148036100595, 0.1095755475481476, 0.8630127527658954, 0.01464021932495108,
  0.01464021932495353, 0.012771480361006, 0.8630127527659015, 0.109575547548139,
  0.01034990660067171, 0.7426915834872547, 0.01167275911784623, 0.2352857507942273,
  0.2352857507942327, 0.01034990660067426, 0.0116727591178434, 0.7426915834872496,
  0.7426915834872502, 0.2352857507942241, 0.01167275911784928, 0.01034990660067648,
  0.0133390399676393, 0.3718583817617002, 0.6057046365583734, 0.009097941712287172,
  0.3718583817617083, 0.009097941712290891, 0.6057046365583626, 0.01333903996763819,
  0.009097941712294314, 0.01333903996763977, 0.6057046365583639, 0.3718583817617021,
  0.5249771861414798, 0.01367226401253988, 0.01029208189692955, 0.4510584679490507,
  0.01367226401254362, 0.4510584679490587, 0.01029208189693136, 0.5249771861414664,
  0.4510584679490486, 0.5249771861414734, 0.01029208189693373, 0.01367226401254431,
  0.0745911424654928, 0.09342069694332726, 0.004110311725985602, 0.8278778488651943,
  0.8278778488651856, 0.07459114246549663, 0.004110311725986349, 0.09342069694333147,
  0.0934206969433283, 0.8278778488651842, 0.004110311725989205, 0.07459114246549824,
  0.0122514981411758, 0.11081079369917, 0.01880574820318091, 0.8581319599564733,
  0.1108107936991686, 0.8581319599564727, 0.01880574820318023, 0.01225149814117846,
  0.85813195995647, 0.01225149814117781, 0.01880574820318224, 0.11081079369917,
  0.01511843542458239, 0.04765944606068975, 0.0750995589695265, 0.8621225595452015,
  0.04765944606069021, 0.8621225595452037, 0.07509955896952418, 0.01511843542458198,
  0.8621225595452005, 0.01511843542458308, 0.0750995589695319, 0.04765944606068458,
  0.1361581213833478, 0.001922023464433764, 0.2260822299666647, 0.6358376251855538,
  0.6358376251855543, 0.13615812138335, 0.2260822299666622, 0.001922023464433459,
  0.001922023464443689, 0.6358376251855318, 0.2260822299666766, 0.1361581213833479,
  0.01376037881840447, 0.7415160297079681, 0.2282126571617323, 0.01651093431189504,
  0.741516029707964, 0.01651093431189725, 0.2282126571617314, 0.01376037881840728,
  0.01651093431189804, 0.01376037881840719, 0.2282126571617405, 0.7415160297079542,
  0.5287234935734707, 0.3829175522239497, 0.08835752618992757, 0.000001428012651988331,
  0.000001428012658284353, 0.5287234935734723, 0.08835752618992139, 0.3829175522239481,
  0.382917552223954, 0.000001428012662889333, 0.0883575261899238, 0.5287234935734594,
  0.8603078190745503, 0.1006669391238628, 0.02182336879483741, 0.0172018730067494,
  0.1006669391238637, 0.01720187300674862, 0.02182336879483792, 0.8603078190745498,
  0.01720187300674926, 0.8603078190745502, 0.0218233687948384, 0.1006669391238621,
  0.213749749548486, 0.003009152671000964, 0.6883673506451037, 0.0948737471354093,
  0.003009152671001727, 0.09487374713541114, 0.6883673506451042, 0.2137497495484828,
  0.09487374713541051, 0.213749749548485, 0.6883673506450955, 0.003009152671008986,
  0.01776885891901024, 0.5596471440071771, 0.4090155222479943, 0.01356847482581836,
  0.5596471440071775, 0.01356847482581952, 0.4090155222479928, 0.01776885891901014,
  0.01356847482581988, 0.01776885891900956, 0.4090155222479974, 0.5596471440071731,
  0.5561861612025368, 0.07185958939197906, 0.3631251266370949, 0.008829122768389208,
  0.07185958939199275, 0.008829122768390513, 0.3631251266370967, 0.5561861612025201,
  0.008829122768396735, 0.556186161202529, 0.3631251266370916, 0.07185958939198267,
  0.02153556644467808, 0.01948609324379375, 0.7368319066698201, 0.2221464336417081,
  0.01948609324379522, 0.2221464336417116, 0.7368319066698122, 0.02153556644468091,
  0.2221464336417159, 0.02153556644468099, 0.736831906669808, 0.01948609324379502,
  0.7706018404420292, 0.01488093241522564, 0.1457507819888409, 0.06876644515390423,
  0.01488093241522547, 0.06876644515390219, 0.1457507819888461, 0.7706018404420262,
  0.06876644515390468, 0.7706018404420206, 0.1457507819888496, 0.01488093241522501,
  0.2632140692833737, 0.5416447947584936, 0.1940096424521396, 0.001131493505993147,
  0.5416447947584961, 0.001131493505992412, 0.1940096424521405, 0.263214069283371,
  0.001131493505999361, 0.2632140692833789, 0.1940096424521402, 0.5416447947584815,
  0.5866866785337993, 0.3700027679954775, 0.01920458791743641, 0.02410596555328681,
  0.02410596555328862, 0.5866866785337975, 0.01920458791743763, 0.3700027679954763,
  0.3700027679954874, 0.02410596555328817, 0.01920458791743828, 0.5866866785337862,
  0.1007245253786872, 0.007839833208067415, 0.681257697378422, 0.2101779440348234,
  0.007839833208073724, 0.2101779440348198, 0.6812576973784202, 0.1007245253786863,
  0.2101779440348183, 0.1007245253786925, 0.6812576973784144, 0.007839833208074687,
  0.2678058473170444, 0.009653727838177417, 0.3203870289323185, 0.4021533959124597,
  0.009653727838177781, 0.4021533959124907, 0.3203870289323026, 0.2678058473170289,
  0.4021533959124549, 0.2678058473170257, 0.3203870289323365, 0.009653727838182913,
  0.01871950766556472, 0.07877407681846821, 0.8174647095402787, 0.08504170597568828,
  0.07877407681846901, 0.08504170597569094, 0.8174647095402758, 0.01871950766556418,
  0.08504170597569295, 0.01871950766556529, 0.8174647095402776, 0.07877407681846416,
  0.2289622580755599, 0.7059180690514001, 0.01703231872933662, 0.04808735414370337,
  0.7059180690513981, 0.04808735414370217, 0.01703231872933689, 0.2289622580755628,
  0.04808735414368957, 0.2289622580755674, 0.01703231872933699, 0.7059180690514061,
  0.01343952012215375, 0.188978322150464, 0.07671766832162848, 0.7208644894057537,
  0.1889783221504602, 0.7208644894057589, 0.07671766832162524, 0.01343952012215571,
  0.7208644894057502, 0.01343952012215593, 0.07671766832162946, 0.1889783221504644,
  0.1856695714205305, 0.00940743474102812, 0.498715106027506, 0.3062078878109354,
  0.3062078878109278, 0.1856695714205285, 0.4987151060275142, 0.009407434741029452,
  0.009407434741032658, 0.306207887810909, 0.4987151060275297, 0.1856695714205286,
  0.07134313304985408, 0.7168988880207371, 0.01586351574919136, 0.1958944631802175,
  0.7168988880207331, 0.1958944631802114, 0.01586351574919187, 0.07134313304986359,
  0.1958944631802093, 0.07134313304985869, 0.01586351574919585, 0.7168988880207361,
  0.6081230921397938, 0.01132540328384632, 0.2960917880883974, 0.08445971648796252,
  0.01132540328384961, 0.08445971648796122, 0.2960917880884005, 0.6081230921397887,
  0.08445971648796277, 0.6081230921397877, 0.2960917880884, 0.01132540328384951,
  0.7831901908047053, 0.08946628745362917, 0.1093980943900156, 0.01794542735164988,
  0.01794542735164876, 0.7831901908046981, 0.1093980943900213, 0.08946628745363189,
  0.08946628745363563, 0.01794542735165081, 0.1093980943900156, 0.783190190804698,
  0.5244117804550043, 0.2084577994081171, 0.01133447823052404, 0.2557959419063546,
  0.2084577994081089, 0.255795941906351, 0.01133447823052516, 0.524411780455015,
  0.2557959419063432, 0.5244117804550297, 0.01133447823052761, 0.2084577994080996,
  0.01588261437502311, 0.3863456880386881, 0.5325804036187812, 0.06519129396750756,
  0.06519129396751876, 0.0158826143750247, 0.5325804036187707, 0.3863456880386859,
  0.3863456880386817, 0.0651912939675148, 0.5325804036187769, 0.01588261437502658,
  0.03236911071658531, 0.6667349326998179, 0.2320665678040404, 0.06882938877955636,
  0.06882938877957372, 0.03236911071658261, 0.2320665678040363, 0.6667349326998073,
  0.6667349326998023, 0.06882938877957215, 0.2320665678040363, 0.03236911071658921,
  0.2154208621405496, 0.01783785666517354, 0.07794412055941285, 0.688797160634864,
  0.01783785666517584, 0.6887971606348672, 0.07794412055941696, 0.2154208621405401,
  0.6887971606348626, 0.2154208621405385, 0.07794412055942193, 0.01783785666517695,
  0.4031765079784496, 0.01499093171087654, 0.5021066311640049, 0.07972592914666898,
  0.01499093171087712, 0.07972592914667045, 0.5021066311640021, 0.4031765079784504,
  0.07972592914666891, 0.4031765079784464, 0.5021066311640048, 0.01499093171087995,
  0.1848636811678036, 0.6499516355495718, 0.0182999648331871, 0.1468847184494375,
  0.6499516355495523, 0.1468847184494371, 0.01829996483318704, 0.1848636811678236,
  0.1468847184494266, 0.184863681167814, 0.01829996483318721, 0.6499516355495722,
  0.1804453441648688, 0.451820102412822, 0.3540241023636928, 0.0137104510586164,
  0.01371045105861957, 0.1804453441648663, 0.3540241023636804, 0.4518201024128338,
  0.4518201024128161, 0.01371045105861805, 0.3540241023636947, 0.1804453441648712,
  0.08105206237388583, 0.3766532156247404, 0.01518945086644218, 0.5271052711349316,
  0.5271052711349223, 0.08105206237388458, 0.01518945086644177, 0.3766532156247513,
  0.3766532156247387, 0.5271052711349294, 0.01518945086644269, 0.08105206237388923,
  0.331408497762104, 0.1126435977537889, 0.0134868064234796, 0.5424610980606277,
  0.5424610980606107, 0.3314084977621181, 0.01348680642347998, 0.1126435977537912,
  0.1126435977537936, 0.5424610980606109, 0.01348680642348059, 0.3314084977621148,
  0.5607935139776807, 0.01909773271486895, 0.06348929065765115, 0.3566194626497992,
  0.01909773271486825, 0.3566194626497967, 0.06348929065765373, 0.5607935139776813,
  0.3566194626497901, 0.5607935139776836, 0.0634892906576574, 0.01909773271486892,
  0.07227368768344591, 0.2738988990502447, 0.6053416400059596, 0.04848577326034986,
  0.04848577326034448, 0.07227368768344192, 0.6053416400059548, 0.2738988990502588,
  0.2738988990502546, 0.04848577326034462, 0.6053416400059433, 0.07227368768345743,
  0.3706144545187708, 0.01602307963396246, 0.1897016601820003, 0.4236608056652664,
  0.01602307963396413, 0.4236608056652554, 0.1897016601819962, 0.3706144545187843,
  0.4236608056652498, 0.3706144545187751, 0.1897016601820099, 0.01602307963396518,
  0.07313934036770678, 0.06778253195192757, 0.7047038738820789, 0.1543742537982867,
  0.1543742537982787, 0.0731393403677088, 0.7047038738820692, 0.06778253195194317,
  0.06778253195194402, 0.1543742537982604, 0.7047038738820758, 0.07313934036771974,
  0.2255550687888375, 0.3828261323216449, 0.01264429188566553, 0.3789745070038521,
  0.3828261323216364, 0.3789745070038535, 0.01264429188566583, 0.2255550687888442,
  0.3789745070038492, 0.2255550687888252, 0.01264429188566767, 0.3828261323216579,
  0.01610664762850615, 0.1955976722408662, 0.504888949609758, 0.2834067305208696,
  0.1955976722408699, 0.2834067305208563, 0.5048889496097685, 0.01610664762850533,
  0.2834067305208526, 0.01610664762850647, 0.5048889496097625, 0.1955976722408784,
  0.07394396840975409, 0.08972209215481677, 0.06088720165051376, 0.7754467377849155,
  0.7754467377849116, 0.07394396840975978, 0.06088720165051331, 0.08972209215481533,
  0.08972209215481254, 0.7754467377849096, 0.06088720165051947, 0.07394396840975842,
  0.02198550415554825, 0.4522698873067332, 0.3656528451019294, 0.1600917634357892,
  0.4522698873067705, 0.1600917634357737, 0.3656528451019036, 0.02198550415555212,
  0.1600917634358059, 0.02198550415555332, 0.3656528451018906, 0.4522698873067502,
  0.6425340162574237, 0.03023340240085394, 0.1777342490770398, 0.1494983322646826,
  0.1494983322647011, 0.6425340162574126, 0.1777342490770339, 0.0302334024008524,
  0.03023340240085156, 0.1494983322646933, 0.1777342490770401, 0.642534016257415,
  0.2982386203137134, 0.3492984375384283, 0.3282766894848435, 0.02418625266301483,
  0.02418625266301134, 0.2982386203137263, 0.3282766894848561, 0.3492984375384063,
  0.3492984375384166, 0.02418625266301722, 0.3282766894848335, 0.2982386203137327,
  0.02492578585848872, 0.5613484323473249, 0.1898351044830521, 0.2238906773111343,
  0.2238906773111161, 0.02492578585848644, 0.1898351044830608, 0.5613484323473367,
  0.5613484323473145, 0.22389067731113, 0.1898351044830645, 0.02492578585849109,
  0.1769461529053036, 0.05090872345953187, 0.6068946490861404, 0.1652504745490241,
  0.1652504745490214, 0.1769461529053149, 0.6068946490861201, 0.05090872345954356,
  0.05090872345953583, 0.1652504745490102, 0.6068946490861318, 0.1769461529053222,
  0.267326785868413, 0.09253312310838845, 0.162728234374953, 0.4774118566482455,
  0.09253312310841946, 0.4774118566482484, 0.1627282343749322, 0.2673267858684,
  0.4774118566482272, 0.2673267858684251, 0.162728234374927, 0.09253312310842074,
  0.6324086041104882, 0.194821777558372, 0.07976498347271095, 0.09300463485842884,
  0.09300463485842678, 0.6324086041104942, 0.0797649834727117, 0.1948217775583673,
  0.1948217775583615, 0.09300463485842231, 0.07976498347272819, 0.632408604110488,
  0.1286081121536503, 0.06206882668877994, 0.5069361346327252, 0.3023869265248444,
  0.3023869265248393, 0.1286081121536543, 0.5069361346327149, 0.06206882668879155,
  0.06206882668879442, 0.3023869265248427, 0.5069361346327274, 0.1286081121536355,
  0.0670060501118351, 0.07446918750056565, 0.362874044201665, 0.4956507181859342,
  0.4956507181859352, 0.06700605011182939, 0.3628740442016639, 0.07446918750057152,
  0.07446918750057789, 0.4956507181859199, 0.3628740442016637, 0.06700605011183852,
  0.04935190074328522, 0.3139246227522204, 0.1497252367121568, 0.4869982397923375,
  0.3139246227522261, 0.4869982397923315, 0.1497252367121615, 0.04935190074328091,
  0.4869982397923459, 0.04935190074327669, 0.149725236712158, 0.3139246227522194,
  0.1083529025389752, 0.08656298623704123, 0.1758982241285937, 0.6291858870953898,
  0.629185887095386, 0.1083529025389925, 0.1758982241285794, 0.08656298623704209,
  0.08656298623703901, 0.629185887095383, 0.1758982241285948, 0.1083529025389832,
  0.4947915054658847, 0.3668061114674768, 0.0797762381765776, 0.05862614489006095,
  0.05862614489007139, 0.4947915054658749, 0.07977623817658046, 0.3668061114674733,
  0.3668061114674683, 0.05862614489007745, 0.07977623817658072, 0.4947915054658735,
  0.6107564898848346, 0.09155687274905353, 0.08682921283620239, 0.2108574245299095,
  0.2108574245299135, 0.6107564898848316, 0.0868292128362, 0.09155687274905493,
  0.09155687274905454, 0.2108574245299094, 0.08682921283620657, 0.6107564898848294,
  0.27189840912706, 0.2718984091270191, 0.1843047726189553, 0.2718984091269656,
  0.08364528610473303, 0.4598959913496589, 0.2836943220226789, 0.1727644005229292,
  0.4598959913496499, 0.1727644005229201, 0.2836943220226703, 0.08364528610475974,
  0.1727644005229245, 0.0836452861047611, 0.2836943220226696, 0.4598959913496448,
  0.220307180915872, 0.2203071809158613, 0.3390784572525623, 0.2203071809157044,
  0.4498492745599813, 0.1402964159526019, 0.06810558755187382, 0.3417487219355428,
  0.3417487219355564, 0.4498492745599653, 0.0681055875518764, 0.1402964159526019,
  0.1402964159526053, 0.3417487219355464, 0.06810558755187403, 0.4498492745599743,
  0.4796245561760771, 0.06988987460087778, 0.2572931400794461, 0.193192429143599,
  0.1931924291436032, 0.4796245561760668, 0.2572931400794509, 0.06988987460087914,
  0.06988987460089365, 0.1931924291436036, 0.2572931400794577, 0.479624556176045,
  0.4819852013641325, 0.2605590256904803, 0.06519355736441289, 0.1922622155809742,
  0.260559025690468, 0.1922622155809665, 0.06519355736441458, 0.481985201364151,
  0.1922622155809799, 0.481985201364128, 0.06519355736441629, 0.2605590256904758,
  0.09109001795840514, 0.343030573977829, 0.2354338687541656, 0.3304455393096003,
  0.3304455393096081, 0.09109001795841783, 0.2354338687541547, 0.3430305739778192,
  0.343030573977809, 0.3304455393095925, 0.2354338687541694, 0.09109001795842916,
  0.08624240167701186, 0.1525520261883117, 0.4323311285083857, 0.3288744436262907,
  0.3288744436262873, 0.0862424016770105, 0.4323311285083789, 0.1525520261883234,
  0.1525520261883389, 0.3288744436262735, 0.4323311285083771, 0.08624240167701047,
  0.3337847727363109, 0.3372700741462638, 0.1536568898623008, 0.1752882632551245,
  0.3372700741462386, 0.1752882632551174, 0.1536568898623003, 0.3337847727363437,
  0.1752882632551262, 0.333784772736308, 0.1536568898623202, 0.3372700741462455,
  0.3113177461109946, 0.3113177461109871, 0.06604676166701309, 0.3113177461110053,
  0.2898527003164425, 0.2359060680311884, 0.3891009454304513, 0.08514028622191777,
  0.2359060680311902, 0.08514028622192746, 0.3891009454304601, 0.2898527003164222,
  0.0851402862219274, 0.2898527003164147, 0.38910094543047, 0.2359060680311879,
  0.1915586123296988, 0.4738597830753307, 0.1624688668332693, 0.1721127377617013,
  0.4738597830753175, 0.1721127377617093, 0.1624688668332666, 0.1915586123297066,
  0.1721127377617219, 0.1915586123296906, 0.1624688668332857, 0.4738597830753017,
  0.343066772448071, 0.1725513660667974, 0.2910280425505992, 0.1933538189345324,
  0.1933538189344859, 0.3430667724481031, 0.2910280425505916, 0.1725513660668194,
  0.1725513660668472, 0.1933538189345398, 0.2910280425506466, 0.3430667724479664,
  0.1627284320161738, 0.1627284320161655, 0.5118147039514781, 0.1627284320161825,
};
const double tetrahedronRule15Weights[] = {
  0.0003056969967675392,
  0.0003056969967677529,
  0.0003056969967681826,
  0.0004854946815200308,
  0.0004854946815204648,
  0.0004854946815205046,
  0.000540231508089061,
  0.0005402315080893089,
  0.0005402315080893216,
  0.0006658073061313105,
  0.000665807306131382,
  0.0006658073061313881,
  0.0008580677785378436,
  0.0008580677785378866,
  0.0008580677785379431,
  0.0008614116841663662,
  0.0008614116841664157,
  0.000861411684166711,
  0.001022857153872907,
  0.00102285715387307,
  0.001022857153873352,
  0.001067732783063372,
  0.001067732783063678,
  0.001067732783063917,
  0.001127475060480442,
  0.001127475060480499,
  0.001127475060480686,
  0.001131195261071419,
  0.001131195261071527,
  0.001131195261071613,
  0.001220520643534932,
  0.001220520643534937,
  0.001220520643535107,
  0.001429872152287352,
  0.001429872152287716,
  0.001429872152288791,
  0.001482149442565798,
  0.001482149442566192,
  0.001482149442566206,
  0.00155092314083083,
  0.001550923140831266,
  0.001550923140831712,
  0.001593499385594808,
  0.001593499385594812,
  0.001593499385594864,
  0.001786124981508196,
  0.001786124981508356,
  0.001786124981509098,
  0.001793662924059105,
  0.001793662924059139,
  0.001793662924059193,
  0.001923299718752182,
  0.001923299718752746,
  0.001923299718753172,
  0.002011193038001121,
  0.002011193038001399,
  0.002011193038001518,
  0.002145067125715038,
  0.002145067125715266,
  0.002145067125715382,
  0.002259956184833013,
  0.002259956184833064,
  0.002259956184833895,
  0.002502336027424191,
  0.00250233602742444,
  0.002502336027424529,
  0.002524144856161971,
  0.002524144856162738,
  0.002524144856163086,
  0.002642042663514365,
  0.002642042663514703,
  0.002642042663516116,
  0.002706105653967578,
  0.002706105653967593,
  0.002706105653967675,
  0.002885552163891226,
  0.002885552163891232,
  0.002885552163891362,
  0.002953010108381281,
  0.002953010108381412,
  0.002953010108381639,
  0.002983590683044804,
  0.002983590683045283,
  0.002983590683046027,
  0.00302772576899869,
  0.003027725768998906,
  0.003027725768999417,
  0.003032163997553845,
  0.003032163997554297,
  0.0030321639975545,
  0.003044930460448902,
  0.003044930460448908,
  0.003044930460449175,
  0.003177770176097537,
  0.003177770176097727,
  0.003177770176098164,
  0.00357683467377095,
  0.003576834673771061,
  0.00357683467377161,
  0.003637919636949187,
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  0.01096256609142445,
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  0.01229675142111412,
  0.01229675142111414,
  0.01229675142112366,
  0.01444493731864532,
};
} // namespace
} // namespace XiaoGimbutas
 
namespace XiaoGimbutas {
const Rule triangleRules[triangleRuleCount] = {
  {1, 3, triangleRule1Points, triangleRule1Weights},
  {3, 3, triangleRule2Points, triangleRule2Weights},
  {6, 3, triangleRule3Points, triangleRule3Weights},
  {6, 3, triangleRule4Points, triangleRule4Weights},
  {7, 3, triangleRule5Points, triangleRule5Weights},
  {12, 3, triangleRule6Points, triangleRule6Weights},
  {15, 3, triangleRule7Points, triangleRule7Weights},
  {16, 3, triangleRule8Points, triangleRule8Weights},
  {19, 3, triangleRule9Points, triangleRule9Weights},
  {25, 3, triangleRule10Points, triangleRule10Weights},
  {28, 3, triangleRule11Points, triangleRule11Weights},
  {33, 3, triangleRule12Points, triangleRule12Weights},
  {37, 3, triangleRule13Points, triangleRule13Weights},
  {42, 3, triangleRule14Points, triangleRule14Weights},
  {49, 3, triangleRule15Points, triangleRule15Weights},
  {55, 3, triangleRule16Points, triangleRule16Weights},
  {60, 3, triangleRule17Points, triangleRule17Weights},
  {67, 3, triangleRule18Points, triangleRule18Weights},
  {73, 3, triangleRule19Points, triangleRule19Weights},
  {79, 3, triangleRule20Points, triangleRule20Weights},
  {87, 3, triangleRule21Points, triangleRule21Weights},
  {96, 3, triangleRule22Points, triangleRule22Weights},
  {103, 3, triangleRule23Points, triangleRule23Weights},
  {112, 3, triangleRule24Points, triangleRule24Weights},
  {120, 3, triangleRule25Points, triangleRule25Weights},
  {130, 3, triangleRule26Points, triangleRule26Weights},
  {141, 3, triangleRule27Points, triangleRule27Weights},
  {150, 3, triangleRule28Points, triangleRule28Weights},
  {159, 3, triangleRule29Points, triangleRule29Weights},
  {171, 3, triangleRule30Points, triangleRule30Weights},
};
 
const Rule tetrahedronRules[tetrahedronRuleCount] = {
  {1, 4, tetrahedronRule1Points, tetrahedronRule1Weights},
  {4, 4, tetrahedronRule2Points, tetrahedronRule2Weights},
  {6, 4, tetrahedronRule3Points, tetrahedronRule3Weights},
  {11, 4, tetrahedronRule4Points, tetrahedronRule4Weights},
  {14, 4, tetrahedronRule5Points, tetrahedronRule5Weights},
  {23, 4, tetrahedronRule6Points, tetrahedronRule6Weights},
  {31, 4, tetrahedronRule7Points, tetrahedronRule7Weights},
  {44, 4, tetrahedronRule8Points, tetrahedronRule8Weights},
  {57, 4, tetrahedronRule9Points, tetrahedronRule9Weights},
  {74, 4, tetrahedronRule10Points, tetrahedronRule10Weights},
  {95, 4, tetrahedronRule11Points, tetrahedronRule11Weights},
  {122, 4, tetrahedronRule12Points, tetrahedronRule12Weights},
  {146, 4, tetrahedronRule13Points, tetrahedronRule13Weights},
  {177, 4, tetrahedronRule14Points, tetrahedronRule14Weights},
  {214, 4, tetrahedronRule15Points, tetrahedronRule15Weights},
};
 
const Rule *getTriangleRule(const int order) {
  if (order < 0 || order > triangleRuleCount)
    return nullptr;
  return &triangleRules[(order > 0 ? order : 1) - 1];
}
 
const Rule *getTetrahedronRule(const int order) {
  if (order < 0 || order > tetrahedronRuleCount)
    return nullptr;
  return &tetrahedronRules[(order > 0 ? order : 1) - 1];
}
} // namespace XiaoGimbutas
 
} // namespace IntRules
 
} // namespace MoFEM