#ifndef ALGOIM_GAUSSQUAD_HPP #define ALGOIM_GAUSSQUAD_HPP // Gaussian quadrature schemes for the interval [0,1] of node count p, 1 <= p <= 100. #include #include "real.hpp" namespace algoim { // Gaussian quadrature schemes for the interval [0,1] of node count p, 1 <= p <= 100. struct GaussQuad { static constexpr int p_max = 100; // Corresponding to the degree p Gaussian quadrature scheme for the interval [0,1], position of node i, 0 <= i < p. static real x(int p, int i) { assert(1 <= p && p <= p_max && 0 <= i && i < p); return data()[p*(p-1) + i]; } // Corresponding to the degree p Gaussian quadrature scheme for the interval [0,1], weight of node i, 0 <= i < p. static real w(int p, int i) { assert(1 <= p && p <= p_max && 0 <= i && i < p); return data()[p*p + i]; } static const real* data() { static_assert(std::is_same_v || std::is_same_v, "Algoim: it looks like you're trying to use high-precision arithmetic, however the precomputed Gaussian quadrature schemes are only accurate to ~20 digits"); // Around 20 digits of accuracy static const real data_[] = { 0.5,1., 0.21132486540518711775,0.78867513459481288225,0.5,0.5, 0.11270166537925831148,0.5,0.88729833462074168852,0.27777777777777777778,0.44444444444444444444,0.27777777777777777778, 0.069431844202973712388,0.3300094782075718676,0.6699905217924281324,0.93056815579702628761,0.17392742256872692869,0.32607257743127307131,0.32607257743127307131,0.17392742256872692869, 0.046910077030668003601,0.23076534494715845448,0.5,0.76923465505284154552,0.9530899229693319964,0.11846344252809454376,0.23931433524968323402,0.28444444444444444444,0.23931433524968323402,0.11846344252809454376, 0.033765242898423986094,0.16939530676686774317,0.38069040695840154568,0.61930959304159845432,0.83060469323313225683,0.96623475710157601391,0.08566224618958517252,0.18038078652406930378,0.23395696728634552369,0.23395696728634552369,0.18038078652406930378,0.08566224618958517252, 0.025446043828620737737,0.12923440720030278007,0.29707742431130141655,0.5,0.70292257568869858345,0.87076559279969721993,0.97455395617137926226,0.064742483084434846635,0.13985269574463833395,0.19091502525255947248,0.20897959183673469388,0.19091502525255947248,0.13985269574463833395,0.064742483084434846635, 0.019855071751231884158,0.1016667612931866302,0.23723379504183550709,0.40828267875217509753,0.59171732124782490247,0.76276620495816449291,0.8983332387068133698,0.98014492824876811584,0.050614268145188129576,0.11119051722668723527,0.15685332293894364367,0.18134189168918099148,0.18134189168918099148,0.15685332293894364367,0.11119051722668723527,0.050614268145188129576, 0.015919880246186955082,0.08198444633668210285,0.19331428364970480135,0.33787328829809553548,0.5,0.66212671170190446452,0.80668571635029519865,0.91801555366331789715,0.98408011975381304492,0.040637194180787205986,0.090324080347428702029,0.13030534820146773116,0.15617353852000142003,0.16511967750062988158,0.15617353852000142003,0.13030534820146773116,0.090324080347428702029,0.040637194180787205986, 0.013046735741414139961,0.067468316655507744634,0.16029521585048779688,0.2833023029353764046,0.42556283050918439456,0.57443716949081560544,0.7166976970646235954,0.83970478414951220312,0.93253168334449225537,0.98695326425858586004,0.033335672154344068797,0.074725674575290296573,0.109543181257991022,0.13463335965499817755,0.14776211235737643509,0.14776211235737643509,0.13463335965499817755,0.109543181257991022,0.074725674575290296573,0.033335672154344068797, 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0.0092196828766403746547,0.047941371814762571661,0.11504866290284765648,0.20634102285669127635,0.31608425050090990312,0.43738329574426554226,0.56261670425573445774,0.68391574949909009688,0.79365897714330872365,0.88495133709715234352,0.95205862818523742834,0.99078031712335962535,0.023587668193255913597,0.05346966299765921548,0.080039164271673113167,0.10158371336153296087,0.11674626826917740438,0.1245735229067013925,0.1245735229067013925,0.11674626826917740438,0.10158371336153296087,0.080039164271673113167,0.05346966299765921548,0.023587668193255913597, 0.0079084726407059252636,0.041200800388511017397,0.099210954633345043603,0.17882533027982988968,0.27575362448177657356,0.38477084202243260297,0.5,0.61522915797756739703,0.72424637551822342644,0.82117466972017011032,0.9007890453666549564,0.9587991996114889826,0.99209152735929407474,0.02024200238265793976,0.046060749918864223957,0.069436755109893619232,0.08907299038097286914,0.10390802376844425116,0.11314159013144861921,0.1162757766154369551,0.11314159013144861921,0.10390802376844425116,0.08907299038097286914,0.069436755109893619232,0.046060749918864223957,0.02024200238265793976, 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0.0060037409897572857552,0.031363303799647047846,0.0758967082947863919,0.13779113431991497629,0.21451391369573057623,0.30292432646121831505,0.39940295300128273885,0.5,0.60059704699871726115,0.69707567353878168495,0.78548608630426942377,0.86220886568008502371,0.9241032917052136081,0.96863669620035295215,0.99399625901024271424,0.015376620998058634177,0.035183023744054062355,0.053579610233585967506,0.069785338963077157224,0.083134602908496966777,0.093080500007781105513,0.099215742663555788228,0.10128912096278063644,0.099215742663555788228,0.093080500007781105513,0.083134602908496966777,0.069785338963077157224,0.053579610233585967506,0.035183023744054062355,0.015376620998058634177, 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}; return data_; } }; } // namespace algoim #endif