test_tr1.cpp

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   BOOST_CHECK(tr1::copysign(-1.0f, 1.0f) == 1.0f);
   BOOST_CHECK(tr1::copysign(-1.0f, -1.0f) == -1.0f);

   BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(0.125)), static_cast<float>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(0.5)), static_cast<float>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(1)), static_cast<float>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(5)), static_cast<float>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(-0.125)), static_cast<float>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(-0.5)), static_cast<float>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(0)), static_cast<float>(1), eps * 1000);

   BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(0.125)), static_cast<float>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(0.5)), static_cast<float>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(1)), static_cast<float>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(5)), static_cast<float>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(-0.125)), static_cast<float>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(-0.5)), static_cast<float>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(0)), static_cast<float>(0), eps * 1000);

   BOOST_CHECK_CLOSE(tr1::log1p(static_cast<float>(0.582029759883880615234375e0)), static_cast<float>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::expm1(static_cast<float>(0.582029759883880615234375e0)), static_cast<float>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::log1p(static_cast<float>(-0.2047410048544406890869140625e-1)), static_cast<float>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
   BOOST_CHECK_CLOSE(tr1::expm1(static_cast<float>(-0.2047410048544406890869140625e-1)), static_cast<float>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);

   BOOST_CHECK_EQUAL(tr1::fmax(0.1f, -0.1f), 0.1f);
   BOOST_CHECK_EQUAL(tr1::fmin(0.1f, -0.1f), -0.1f);

   BOOST_CHECK_CLOSE(tr1::hypot(1.0f, 3.0f), std::sqrt(10.0f), eps * 500);

   BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(3.5)), static_cast<float>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
   BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(0.125)), static_cast<float>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
   BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(-0.125)), static_cast<float>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
   BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(-3.125)), static_cast<float>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
   BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(-53249.0/1024)), static_cast<float>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);

   BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(3.5)), static_cast<float>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
   BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(0.125)), static_cast<float>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
   BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(-0.125)), static_cast<float>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
   BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(-3.125)), static_cast<float>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);

#ifdef BOOST_HAS_LONG_LONG
   BOOST_CHECK(tr1::llround(2.5f) == 3LL);
   BOOST_CHECK(tr1::llround(2.25f) == 2LL);
#endif
   BOOST_CHECK(tr1::lround(2.5f) == 3L);
   BOOST_CHECK(tr1::lround(2.25f) == 2L);
   BOOST_CHECK(tr1::round(2.5f) == 3.0f);
   BOOST_CHECK(tr1::round(2.25f) == 2.0f);

   BOOST_CHECK(tr1::nextafter(1.0f, 2.0f) > 1.0f);
   BOOST_CHECK(tr1::nextafter(1.0f, -2.0f) < 1.0f);
   BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, 2.0f), -2.0f) == 1.0f);
   BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, -2.0f), 2.0f) == 1.0f);
   BOOST_CHECK(tr1::nextafter(1.0f, 2.0f) > 1.0f);
   BOOST_CHECK(tr1::nextafter(1.0f, -2.0f) < 1.0f);
   BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, 2.0f), -2.0f) == 1.0f);
   BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, -2.0f), 2.0f) == 1.0f);

   BOOST_CHECK(tr1::trunc(2.5f) == 2.0f);
   BOOST_CHECK(tr1::trunc(2.25f) == 2.0f);

   //
   // Now for the TR1 math functions:
   //
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(4, 5, static_cast<float>(0.5L)), static_cast<float>(88.31510416666666666666666666666666666667L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 0, static_cast<float>(2.5L)), static_cast<float>(-0.8802526766660982969576719576719576719577L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 1, static_cast<float>(4.5L)), static_cast<float>(1.564311458042689732142857142857142857143L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 6, static_cast<float>(8.5L)), static_cast<float>(20.51596541066649098875661375661375661376L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 12, static_cast<float>(12.5L)), static_cast<float>(-199.5560968456234671241181657848324514991L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(50, 40, static_cast<float>(12.5L)), static_cast<float>(-4.996769495006119488583146995907246595400e16L), eps * 100);

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

   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(1, static_cast<float>(-0.5L)), static_cast<float>(1.5L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(4, static_cast<float>(-0.5L)), static_cast<float>(3.835937500000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(7, static_cast<float>(-0.5L)), static_cast<float>(7.950934709821428571428571428571428571429L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(20, static_cast<float>(-0.5L)), static_cast<float>(76.12915699869631476833699787070874048223L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(50, static_cast<float>(-0.5L)), static_cast<float>(2307.428631277506570629232863491518399720L), eps * 100);

   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(1, static_cast<float>(4.5L)), static_cast<float>(-3.500000000000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(4, static_cast<float>(4.5L)), static_cast<float>(0.08593750000000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(7, static_cast<float>(4.5L)), static_cast<float>(-1.036928013392857142857142857142857142857L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(20, static_cast<float>(4.5L)), static_cast<float>(1.437239150257817378525582974722170737587L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(50, static_cast<float>(4.5L)), static_cast<float>(-0.7795068145562651416494321484050019245248L), eps * 100);

   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(4, 2, static_cast<float>(0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(7, 5, static_cast<float>(0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(4, 2, static_cast<float>(-0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(7, 5, static_cast<float>(-0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);

   BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(4, static_cast<float>(0.5L)), static_cast<float>(-0.2890625000000000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(7, static_cast<float>(0.5L)), static_cast<float>(0.2231445312500000000000000000000000000000L), eps * 100);
   BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(40, static_cast<float>(0.5L)), static_cast<float>(-0.09542943523261546936538467572384923220258L), eps * 100);

   float sv = eps / 1024;
   BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(1), static_cast<float>(1)), static_cast<float>(1), eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(1), static_cast<float>(4)), static_cast<float>(0.25), eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(4), static_cast<float>(1)), static_cast<float>(0.25), eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::betaf(sv, static_cast<float>(4)), 1/sv, eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(4), sv), 1/sv, eps * 20 * 100);
   BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(4), static_cast<float>(20)), static_cast<float>(0.00002823263692828910220214568040654997176736L), eps * 20 * 100);