test_tr1.cpp

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   BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(400) / 1024, ldexp(static_cast<float>(1), 66)), static_cast<float>(7.0886102721911705466476846969992069994308167515242e19), eps * 5000);

   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(1), static_cast<float>(-1)), static_cast<float>(-1.557407724654902230506974807458360173087), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.4), static_cast<float>(0), static_cast<float>(-4)), static_cast<float>(-4.153623371196831087495427530365430979011), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(-0.6), static_cast<float>(0), static_cast<float>(8)), static_cast<float>(8.935930619078575123490612395578518914416), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.25), static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(0.501246705365439492445236118603525029757890291780157969500480), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(0.5), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(-2), static_cast<float>(0.5)), static_cast<float>(0.437501067017546278595664813509803743009132067629603474488486), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0.25), static_cast<float>(0.5)), static_cast<float>(0.510269830229213412212501938035914557628394166585442994564135), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0.75), static_cast<float>(0.5)), static_cast<float>(0.533293253875952645421201146925578536430596894471541312806165), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0.75), static_cast<float>(0.75)), static_cast<float>(0.871827580412760575085768367421866079353646112288567703061975), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(1), static_cast<float>(0.25)), static_cast<float>(0.255341921221036266504482236490473678204201638800822621740476), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(2), static_cast<float>(0.25)), static_cast<float>(0.261119051639220165094943572468224137699644963125853641716219), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(1023)/1024, static_cast<float>(1.5)), static_cast<float>(13.2821612239764190363647953338544569682942329604483733197131), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.5), static_cast<float>(0.5), static_cast<float>(-1)), static_cast<float>(-1.228014414316220642611298946293865487807), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.5), static_cast<float>(0.5), static_cast<float>(1e+10)), static_cast<float>(1.536591003599172091573590441336982730551e+10), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.75), static_cast<float>(-1e+05), static_cast<float>(10)), static_cast<float>(0.0347926099493147087821620459290460547131012904008557007934290), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(10)), static_cast<float>(0.000109956202759561502329123384755016959364346382187364656768212), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(1e+20)), static_cast<float>(1.00000626665567332602765201107198822183913978895904937646809e15), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(1608)/1024), static_cast<float>(0.0000157080616044072676127333183571107873332593142625043567690379), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), 1-static_cast<float>(1) / 1024, static_cast<float>(1e+20)), static_cast<float>(6.43274293944380717581167058274600202023334985100499739678963e21), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.25), static_cast<float>(50), static_cast<float>(0.1)), static_cast<float>(0.124573770342749525407523258569507331686458866564082916835900), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.25), static_cast<float>(1.125), static_cast<float>(1)), static_cast<float>(1.77299767784815770192352979665283069318388205110727241629752), eps * 5000);

   BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(1)/1024), static_cast<float>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(0.125)), static_cast<float>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(0.5)), static_cast<float>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(1)), static_cast<float>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(50.5)), static_cast<float>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-1)/1024), static_cast<float>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-0.125)), static_cast<float>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-0.5)), static_cast<float>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-1)), static_cast<float>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-50.5)), static_cast<float>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000);

   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(0, static_cast<float>(1)), static_cast<float>(1.L), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(1)), static_cast<float>(2.L), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(2)), static_cast<float>(4.L), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(10)), static_cast<float>(20), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(100)), static_cast<float>(200), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(1e6)), static_cast<float>(2e6), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(30)), static_cast<float>(5.896624628001300E+17L), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(1000)), static_cast<float>(1.023976960161280E+33L), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(10)), static_cast<float>(8.093278209760000E+12L), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(-10)), static_cast<float>(8.093278209760000E+12L), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(3, static_cast<float>(-10)), static_cast<float>(-7.880000000000000E+3L), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(3, static_cast<float>(-1000)), static_cast<float>(-7.999988000000000E+9L), 100 * eps);
   BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(3, static_cast<float>(-1000000)), static_cast<float>(-7.999999999988000E+18L), 100 * eps);

   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(0.125)), static_cast<float>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(1023) / static_cast<float>(1024)), static_cast<float>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(1025) / static_cast<float>(1024)), static_cast<float>(1024.5772867695045940578681624248887776501597556226L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(0.5)), static_cast<float>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(1.125)), static_cast<float>(8.5862412945105752999607544082693023591996301183069L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(2)), static_cast<float>(1.6449340668482264364724151666460251892189499012068L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(3.5)), static_cast<float>(1.1267338673170566464278124918549842722219969574036L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(4)), static_cast<float>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(4 + static_cast<float>(1) / 1024), static_cast<float>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(4.5)), static_cast<float>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(6.5)), static_cast<float>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(7.5)), static_cast<float>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(8.125)), static_cast<float>(1.0037305205308161603183307711439385250181080293472L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(16.125)), static_cast<float>(1.0000140128224754088474783648500235958510030511915L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(0)), static_cast<float>(-0.5L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-0.125)), static_cast<float>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-1)), static_cast<float>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-2)), static_cast<float>(0L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-2.5)), static_cast<float>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000 * 3);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-3)), static_cast<float>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-4)), static_cast<float>(0), eps * 5000);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-20)), static_cast<float>(0), eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-21)), static_cast<float>(-281.46014492753623188405797101449275362318840579710L), eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-30.125)), static_cast<float>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000 * 100);

   BOOST_CHECK_CLOSE(tr1::sph_besself(0, static_cast<float>(0.1433600485324859619140625e-1)), static_cast<float>(0.9999657468461303487880990241993035937654e0),  eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::sph_besself(0, static_cast<float>(0.1760916970670223236083984375e-1)), static_cast<float>(0.9999483203249623334100130061926184665364e0),  eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::sph_besself(2, static_cast<float>(0.1433600485324859619140625e-1)), static_cast<float>(0.1370120120703995134662099191103188366059e-4),  eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::sph_besself(2, static_cast<float>(0.1760916970670223236083984375e-1)), static_cast<float>(0.2067173265753174063228459655801741280461e-4),  eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::sph_besself(7, static_cast<float>(0.1252804412841796875e3)), static_cast<float>(0.7887555711993028736906736576314283291289e-2),  eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::sph_besself(7, static_cast<float>(0.25554705810546875e3)), static_cast<float>(-0.1463292767579579943284849187188066532514e-2),  eps * 5000 * 100);

   BOOST_CHECK_CLOSE(tr1::sph_neumannf(0, static_cast<float>(0.408089816570281982421875e0)), static_cast<float>(-0.2249212131304610409189209411089291558038e1), eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::sph_neumannf(0, static_cast<float>(0.6540834903717041015625e0)), static_cast<float>(-0.1213309779166084571756446746977955970241e1),   eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::sph_neumannf(2, static_cast<float>(0.408089816570281982421875e0)), static_cast<float>(-0.4541702641837159203058389758895634766256e2),   eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::sph_neumannf(2, static_cast<float>(0.6540834903717041015625e0)), static_cast<float>(-0.1156112621471167110574129561700037138981e2),   eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::sph_neumannf(10, static_cast<float>(0.1097540378570556640625e1)), static_cast<float>(-0.2427889658115064857278886600528596240123e9),   eps * 5000 * 100);
   BOOST_CHECK_CLOSE(tr1::sph_neumannf(10, static_cast<float>(0.30944411754608154296875e1)), static_cast<float>(-0.3394649246350136450439882104151313759251e4),   eps * 5000 * 100);

   BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendref(3, 2, static_cast<float>(0.5)), static_cast<float>(0.2061460599687871330692286791802688341213L), eps * 5000);
   BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendref(40, 15, static_cast<float>(0.75)), static_cast<float>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000);

   //
   // Now all over again but without the "f" suffix on the function names this time:
   //
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(4, 5, static_cast<float>(0.5L)), static_cast<float>(88.31510416666666666666666666666666666667L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 0, static_cast<float>(2.5L)), static_cast<float>(-0.8802526766660982969576719576719576719577L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 1, static_cast<float>(4.5L)), static_cast<float>(1.564311458042689732142857142857142857143L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 6, static_cast<float>(8.5L)), static_cast<float>(20.51596541066649098875661375661375661376L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 12, static_cast<float>(12.5L)), static_cast<float>(-199.5560968456234671241181657848324514991L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(50, 40, static_cast<float>(12.5L)), static_cast<float>(-4.996769495006119488583146995907246595400e16L), eps * 100);

   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<float>(0.5L)), static_cast<float>(-0.3307291666666666666666666666666666666667L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<float>(0.5L)), static_cast<float>(-0.5183392237103174603174603174603174603175L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<float>(0.5L)), static_cast<float>(0.3120174870800154148915399248893113634676L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<float>(0.5L)), static_cast<float>(-0.3181388060269979064951118308575628226834L), eps * 100);