feat: add C implementation for @stdlib/math/base/special/ellipe

This commit introduces a C implementation for the elliptic integral of the second kind (@stdlib/math/base/special/ellipe).

Author: gunjjoshi

Diff for: lib/node_modules/@stdlib/math/base/special/ellipk/scripts/evalpoly.js

@@ -41,215 +41,179 @@ var compileC = require( '@stdlib/math/base/tools/evalpoly-compile-c' );
 
 // Table 2 for expansion about x = 0.05:
 var P1 = [
-	1.591003453790792180,
-	0.416000743991786912,
-	0.245791514264103415,
-	0.179481482914906162,
-	0.144556057087555150,
-	0.123200993312427711,
-	0.108938811574293531,
-	0.098853409871592910,
-	0.091439629201749751,
-	0.085842591595413900,
-	0.081541118718303215
+	1.550973351780472328,
+	-0.400301020103198524,
+	-0.078498619442941939,
+	-0.034318853117591992,
+	-0.019718043317365499,
+	-0.013059507731993309,
+	-0.009442372874146547,
+	-0.007246728512402157,
+	-0.005807424012956090,
+	-0.004809187786009338
 ];
 
 // Table 3 for expansion about 0.15:
 var P2 = [
-	1.635256732264579992,
-	0.471190626148732291,
-	0.309728410831499587,
-	0.252208311773135699,
-	0.226725623219684650,
-	0.215774446729585976,
-	0.213108771877348910,
-	0.216029124605188282,
-	0.223255831633057896,
-	0.234180501294209925,
-	0.248557682972264071,
-	0.266363809892617521
+	1.510121832092819728,
+	-0.417116333905867549,
+	-0.090123820404774569,
+	-0.043729944019084312,
+	-0.027965493064761785,
+	-0.020644781177568105,
+	-0.016650786739707238,
+	-0.014261960828842520,
+	-0.012759847429264803,
+	-0.011799303775587354,
+	-0.011197445703074968
 ];
 
 // Table 4 for expansion about 0.25:
 var P3 = [
-	1.685750354812596043,
-	0.541731848613280329,
-	0.401524438390690257,
-	0.369642473420889090,
-	0.376060715354583645,
-	0.405235887085125919,
-	0.453294381753999079,
-	0.520518947651184205,
-	0.609426039204995055,
-	0.724263522282908870,
-	0.871013847709812357,
-	1.057652872753547036
+	1.467462209339427155,
+	-0.436576290946337775,
+	-0.105155557666942554,
+	-0.057371843593241730,
+	-0.041391627727340220,
+	-0.034527728505280841,
+	-0.031495443512532783,
+	-0.030527000890325277,
+	-0.030916984019238900,
+	-0.032371395314758122,
+	-0.034789960386404158
 ];
 
 // Table 5 for expansion about 0.35:
 var P4 = [
-	1.744350597225613243,
-	0.634864275371935304,
-	0.539842564164445538,
-	0.571892705193787391,
-	0.670295136265406100,
-	0.832586590010977199,
-	1.073857448247933265,
-	1.422091460675497751,
-	1.920387183402304829,
-	2.632552548331654201,
-	3.652109747319039160,
-	5.115867135558865806,
-	7.224080007363877411
+	1.422691133490879171,
+	-0.459513519621048674,
+	-0.125250539822061878,
+	-0.078138545094409477,
+	-0.064714278472050002,
+	-0.062084339131730311,
+	-0.065197032815572477,
+	-0.072793895362578779,
+	-0.084959075171781003,
+	-0.102539850131045997,
+	-0.127053585157696036,
+	-0.160791120691274606
 ];
 
 // Table 6 for expansion about 0.45:
 var P5 = [
-	1.813883936816982644,
-	0.763163245700557246,
-	0.761928605321595831,
-	0.951074653668427927,
-	1.315180671703161215,
-	1.928560693477410941,
-	2.937509342531378755,
-	4.594894405442878062,
-	7.330071221881720772,
-	11.87151259742530180,
-	19.45851374822937738,
-	32.20638657246426863,
-	53.73749198700554656,
-	90.27388602940998849
+	1.375401971871116291,
+	-0.487202183273184837,
+	-0.153311701348540228,
+	-0.111849444917027833,
+	-0.108840952523135768,
+	-0.122954223120269076,
+	-0.152217163962035047,
+	-0.200495323642697339,
+	-0.276174333067751758,
+	-0.393513114304375851,
+	-0.575754406027879147,
+	-0.860523235727239756,
+	-1.308833205758540162
 ];
 
 // Table 7 for expansion about 0.55:
 var P6 = [
-	1.898924910271553526,
-	0.950521794618244435,
-	1.151077589959015808,
-	1.750239106986300540,
-	2.952676812636875180,
-	5.285800396121450889,
-	9.832485716659979747,
-	18.78714868327559562,
-	36.61468615273698145,
-	72.45292395127771801,
-	145.1079577347069102,
-	293.4786396308497026,
-	598.3851815055010179,
-	1228.420013075863451,
-	2536.529755382764488
+	1.325024497958230082,
+	-0.521727647557566767,
+	-0.194906430482126213,
+	-0.171623726822011264,
+	-0.202754652926419141,
+	-0.278798953118534762,
+	-0.420698457281005762,
+	-0.675948400853106021,
+	-1.136343121839229244,
+	-1.976721143954398261,
+	-3.531696773095722506,
+	-6.446753640156048150,
+	-11.97703130208884026
 ];
 
 // Table 8 for expansion about 0.65:
 var P7 = [
-	2.007598398424376302,
-	1.248457231212347337,
-	1.926234657076479729,
-	3.751289640087587680,
-	8.119944554932045802,
-	18.66572130873555361,
-	44.60392484291437063,
-	109.5092054309498377,
-	274.2779548232413480,
-	697.5598008606326163,
-	1795.716014500247129,
-	4668.381716790389910,
-	12235.76246813664335,
-	32290.17809718320818,
-	85713.07608195964685,
-	228672.1890493117096,
-	612757.2711915852774
+	1.270707479650149744,
+	-0.566839168287866583,
+	-0.262160793432492598,
+	-0.292244173533077419,
+	-0.440397840850423189,
+	-0.774947641381397458,
+	-1.498870837987561088,
+	-3.089708310445186667,
+	-6.667595903381001064,
+	-14.89436036517319078,
+	-34.18120574251449024,
+	-80.15895841905397306,
+	-191.3489480762984920,
+	-463.5938853480342030,
+	-1137.380822169360061
 ];
 
 // Table 9 for expansion about 0.75:
 var P8 = [
-	2.156515647499643235,
-	1.791805641849463243,
-	3.826751287465713147,
-	10.38672468363797208,
-	31.40331405468070290,
-	100.9237039498695416,
-	337.3268282632272897,
-	1158.707930567827917,
-	4060.990742193632092,
-	14454.00184034344795,
-	52076.66107599404803,
-	189493.6591462156887,
-	695184.5762413896145,
-	2567994.048255284686,
-	9541921.966748386322,
-	35634927.44218076174,
-	133669298.4612040871,
-	503352186.6866284541,
-	1901975729.538660119,
-	7208915015.330103756
+	1.211056027568459525,
+	-0.630306413287455807,
+	-0.387166409520669145,
+	-0.592278235311934603,
+	-1.237555584513049844,
+	-3.032056661745247199,
+	-8.181688221573590762,
+	-23.55507217389693250,
+	-71.04099935893064956,
+	-221.8796853192349888,
+	-712.1364793277635425,
+	-2336.125331440396407,
+	-7801.945954775964673,
+	-26448.19586059191933,
+	-90799.48341621365251,
+	-315126.0406449163424,
+	-1104011.344311591159
 ];
 
 // Table 10 for expansion about 0.825:
 var P9 = [
-	2.318122621712510589,
-	2.616920150291232841,
-	7.897935075731355823,
-	30.50239715446672327,
-	131.4869365523528456,
-	602.9847637356491617,
-	2877.024617809972641,
-	14110.51991915180325,
-	70621.44088156540229,
-	358977.2665825309926,
-	1847238.263723971684,
-	9600515.416049214109,
-	50307677.08502366879,
-	265444188.6527127967,
-	1408862325.028702687,
-	7515687935.373774627
+	1.161307152196282836,
+	-0.701100284555289548,
+	-0.580551474465437362,
+	-1.243693061077786614,
+	-3.679383613496634879,
+	-12.81590924337895775,
+	-49.25672530759985272,
+	-202.1818735434090269,
+	-869.8602699308701437,
+	-3877.005847313289571,
+	-17761.70710170939814,
+	-83182.69029154232061,
+	-396650.4505013548170,
+	-1920033.413682634405
 ];
 
 // Table 11 for expansion about 0.875:
 var P10 = [
-	2.473596173751343912,
-	3.727624244118099310,
-	15.60739303554930496,
-	84.12850842805887747,
-	506.9818197040613935,
-	3252.277058145123644,
-	21713.24241957434256,
-	149037.0451890932766,
-	1043999.331089990839,
-	7427974.817042038995,
-	53503839.67558661151,
-	389249886.9948708474,
-	2855288351.100810619,
-	21090077038.76684053,
-	156699833947.7902014,
-	1170222242422.439893,
-	8777948323668.937971,
-	66101242752484.95041,
-	499488053713388.7989,
-	37859743397240299.20
+	1.124617325119752213,
+	-0.770845056360909542,
+	-0.844794053644911362,
+	-2.490097309450394453,
+	-10.23971741154384360,
+	-49.74900546551479866,
+	-267.0986675195705196,
+	-1532.665883825229947,
+	-9222.313478526091951,
+	-57502.51612140314030,
+	-368596.1167416106063,
+	-2415611.088701091428,
+	-16120097.81581656797,
+	-109209938.5203089915,
+	-749380758.1942496220,
+	-5198725846.725541393,
+	-36409256888.12139973
 ];
 
-// Table 12 for Maclaurin expansion of Jacobi's nome, q, as a function of the elliptic parameter, m:
+// Table 2 for the expansion of K(m) around 0.05
 var P11 = [
-	0.0,
-	1.0 / 16.0,
-	1.0 / 32.0,
-	21.0 / 1024.0,
-	31.0 / 2048.0,
-	6257.0 / 524288.0,
-	10293.0 / 1048576.0,
-	279025.0 / 33554432.0,
-	483127.0 / 67108864.0,
-	435506703.0 / 68719476736.0,
-	776957575.0 / 137438953472.0,
-	22417045555.0 / 4398046511104.0,
-	40784671953.0 / 8796093022208.0,
-	9569130097211.0 / 2251799813685248.0,
-	17652604545791.0 / 4503599627370496.0
-];
-
-// Talyor expansion of K(m) - E(m) for 0 <= m <= 0.1:
-var P12 = [
 	1.591003453790792180,
 	0.416000743991786912,
 	0.245791514264103415,
@@ -263,6 +227,20 @@ var P12 = [
 	0.081541118718303215
 ];
 
+// Table 2 for the expansion of E(m) around 0.05
+var P12 = [
+	1.550973351780472328,
+	-0.400301020103198524,
+	-0.078498619442941939,
+	-0.034318853117591992,
+	-0.019718043317365499,
+	-0.013059507731993309,
+	-0.009442372874146547,
+	-0.007246728512402157,
+	-0.005807424012956090,
+	-0.004809187786009338
+];
+
 // Header to add to output files:
 var header = licenseHeader( 'Apache-2.0', 'js', {
 	'year': currentYear(),