boost/math/special_functions/trigamma.hpp
// (C) Copyright John Maddock 2006. // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) #ifndef BOOST_MATH_SF_TRIGAMMA_HPP #define BOOST_MATH_SF_TRIGAMMA_HPP #ifdef _MSC_VER #pragma once #endif #include <boost/math/special_functions/math_fwd.hpp> #include <boost/math/tools/rational.hpp> #include <boost/math/tools/series.hpp> #include <boost/math/tools/promotion.hpp> #include <boost/math/policies/error_handling.hpp> #include <boost/math/constants/constants.hpp> #include <boost/math/tools/big_constant.hpp> #include <boost/math/special_functions/polygamma.hpp> #if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128) // // This is the only way we can avoid // warning: non-standard suffix on floating constant [-Wpedantic] // when building with -Wall -pedantic. Neither __extension__ // nor #pragma diagnostic ignored work :( // #pragma GCC system_header #endif namespace boost{ namespace math{ namespace detail{ template<class T, class Policy> T polygamma_imp(const int n, T x, const Policy &pol); template <class T, class Policy> T trigamma_prec(T x, const std::integral_constant<int, 53>*, const Policy&) { // Max error in interpolated form: 3.736e-017 static const T offset = BOOST_MATH_BIG_CONSTANT(T, 53, 2.1093254089355469); static const T P_1_2[] = { BOOST_MATH_BIG_CONSTANT(T, 53, -1.1093280605946045), BOOST_MATH_BIG_CONSTANT(T, 53, -3.8310674472619321), BOOST_MATH_BIG_CONSTANT(T, 53, -3.3703848401898283), BOOST_MATH_BIG_CONSTANT(T, 53, 0.28080574467981213), BOOST_MATH_BIG_CONSTANT(T, 53, 1.6638069578676164), BOOST_MATH_BIG_CONSTANT(T, 53, 0.64468386819102836), }; static const T Q_1_2[] = { BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), BOOST_MATH_BIG_CONSTANT(T, 53, 3.4535389668541151), BOOST_MATH_BIG_CONSTANT(T, 53, 4.5208926987851437), BOOST_MATH_BIG_CONSTANT(T, 53, 2.7012734178351534), BOOST_MATH_BIG_CONSTANT(T, 53, 0.64468798399785611), BOOST_MATH_BIG_CONSTANT(T, 53, -0.20314516859987728e-6), }; // Max error in interpolated form: 1.159e-017 static const T P_2_4[] = { BOOST_MATH_BIG_CONSTANT(T, 53, -0.13803835004508849e-7), BOOST_MATH_BIG_CONSTANT(T, 53, 0.50000049158540261), BOOST_MATH_BIG_CONSTANT(T, 53, 1.6077979838469348), BOOST_MATH_BIG_CONSTANT(T, 53, 2.5645435828098254), BOOST_MATH_BIG_CONSTANT(T, 53, 2.0534873203680393), BOOST_MATH_BIG_CONSTANT(T, 53, 0.74566981111565923), }; static const T Q_2_4[] = { BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), BOOST_MATH_BIG_CONSTANT(T, 53, 2.8822787662376169), BOOST_MATH_BIG_CONSTANT(T, 53, 4.1681660554090917), BOOST_MATH_BIG_CONSTANT(T, 53, 2.7853527819234466), BOOST_MATH_BIG_CONSTANT(T, 53, 0.74967671848044792), BOOST_MATH_BIG_CONSTANT(T, 53, -0.00057069112416246805), }; // Maximum Deviation Found: 6.896e-018 // Expected Error Term : -6.895e-018 // Maximum Relative Change in Control Points : 8.497e-004 static const T P_4_inf[] = { static_cast<T>(0.68947581948701249e-17L), static_cast<T>(0.49999999999998975L), static_cast<T>(1.0177274392923795L), static_cast<T>(2.498208511343429L), static_cast<T>(2.1921221359427595L), static_cast<T>(1.5897035272532764L), static_cast<T>(0.40154388356961734L), }; static const T Q_4_inf[] = { static_cast<T>(1.0L), static_cast<T>(1.7021215452463932L), static_cast<T>(4.4290431747556469L), static_cast<T>(2.9745631894384922L), static_cast<T>(2.3013614809773616L), static_cast<T>(0.28360399799075752L), static_cast<T>(0.022892987908906897L), }; if(x <= 2) { return (offset + boost::math::tools::evaluate_polynomial(P_1_2, x) / tools::evaluate_polynomial(Q_1_2, x)) / (x * x); } else if(x <= 4) { T y = 1 / x; return (1 + tools::evaluate_polynomial(P_2_4, y) / tools::evaluate_polynomial(Q_2_4, y)) / x; } T y = 1 / x; return (1 + tools::evaluate_polynomial(P_4_inf, y) / tools::evaluate_polynomial(Q_4_inf, y)) / x; } template <class T, class Policy> T trigamma_prec(T x, const std::integral_constant<int, 64>*, const Policy&) { // Max error in interpolated form: 1.178e-020 static const T offset_1_2 = BOOST_MATH_BIG_CONSTANT(T, 64, 2.109325408935546875); static const T P_1_2[] = { BOOST_MATH_BIG_CONSTANT(T, 64, -1.10932535608960258341), BOOST_MATH_BIG_CONSTANT(T, 64, -4.18793841543017129052), BOOST_MATH_BIG_CONSTANT(T, 64, -4.63865531898487734531), BOOST_MATH_BIG_CONSTANT(T, 64, -0.919832884430500908047), BOOST_MATH_BIG_CONSTANT(T, 64, 1.68074038333180423012), BOOST_MATH_BIG_CONSTANT(T, 64, 1.21172611429185622377), BOOST_MATH_BIG_CONSTANT(T, 64, 0.259635673503366427284), }; static const T Q_1_2[] = { BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), BOOST_MATH_BIG_CONSTANT(T, 64, 3.77521119359546982995), BOOST_MATH_BIG_CONSTANT(T, 64, 5.664338024578956321), BOOST_MATH_BIG_CONSTANT(T, 64, 4.25995134879278028361), BOOST_MATH_BIG_CONSTANT(T, 64, 1.62956638448940402182), BOOST_MATH_BIG_CONSTANT(T, 64, 0.259635512844691089868), BOOST_MATH_BIG_CONSTANT(T, 64, 0.629642219810618032207e-8), }; // Max error in interpolated form: 3.912e-020 static const T P_2_8[] = { BOOST_MATH_BIG_CONSTANT(T, 64, -0.387540035162952880976e-11), BOOST_MATH_BIG_CONSTANT(T, 64, 0.500000000276430504), BOOST_MATH_BIG_CONSTANT(T, 64, 3.21926880986360957306), BOOST_MATH_BIG_CONSTANT(T, 64, 10.2550347708483445775), BOOST_MATH_BIG_CONSTANT(T, 64, 18.9002075150709144043), BOOST_MATH_BIG_CONSTANT(T, 64, 21.0357215832399705625), BOOST_MATH_BIG_CONSTANT(T, 64, 13.4346512182925923978), BOOST_MATH_BIG_CONSTANT(T, 64, 3.98656291026448279118), }; static const T Q_2_8[] = { BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), BOOST_MATH_BIG_CONSTANT(T, 64, 6.10520430478613667724), BOOST_MATH_BIG_CONSTANT(T, 64, 18.475001060603645512), BOOST_MATH_BIG_CONSTANT(T, 64, 31.7087534567758405638), BOOST_MATH_BIG_CONSTANT(T, 64, 31.908814523890465398), BOOST_MATH_BIG_CONSTANT(T, 64, 17.4175479039227084798), BOOST_MATH_BIG_CONSTANT(T, 64, 3.98749106958394941276), BOOST_MATH_BIG_CONSTANT(T, 64, -0.000115917322224411128566), }; // Maximum Deviation Found: 2.635e-020 // Expected Error Term : 2.635e-020 // Maximum Relative Change in Control Points : 1.791e-003 static const T P_8_inf[] = { BOOST_MATH_BIG_CONSTANT(T, 64, -0.263527875092466899848e-19), BOOST_MATH_BIG_CONSTANT(T, 64, 0.500000000000000058145), BOOST_MATH_BIG_CONSTANT(T, 64, 0.0730121433777364138677), BOOST_MATH_BIG_CONSTANT(T, 64, 1.94505878379957149534), BOOST_MATH_BIG_CONSTANT(T, 64, 0.0517092358874932620529), BOOST_MATH_BIG_CONSTANT(T, 64, 1.07995383547483921121), }; static const T Q_8_inf[] = { BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), BOOST_MATH_BIG_CONSTANT(T, 64, -0.187309046577818095504), BOOST_MATH_BIG_CONSTANT(T, 64, 3.95255391645238842975), BOOST_MATH_BIG_CONSTANT(T, 64, -1.14743283327078949087), BOOST_MATH_BIG_CONSTANT(T, 64, 2.52989799376344914499), BOOST_MATH_BIG_CONSTANT(T, 64, -0.627414303172402506396), BOOST_MATH_BIG_CONSTANT(T, 64, 0.141554248216425512536), }; if(x <= 2) { return (offset_1_2 + boost::math::tools::evaluate_polynomial(P_1_2, x) / tools::evaluate_polynomial(Q_1_2, x)) / (x * x); } else if(x <= 8) { T y = 1 / x; return (1 + tools::evaluate_polynomial(P_2_8, y) / tools::evaluate_polynomial(Q_2_8, y)) / x; } T y = 1 / x; return (1 + tools::evaluate_polynomial(P_8_inf, y) / tools::evaluate_polynomial(Q_8_inf, y)) / x; } template <class T, class Policy> T trigamma_prec(T x, const std::integral_constant<int, 113>*, const Policy&) { // Max error in interpolated form: 1.916e-035 static const T P_1_2[] = { BOOST_MATH_BIG_CONSTANT(T, 113, -0.999999999999999082554457936871832533), BOOST_MATH_BIG_CONSTANT(T, 113, -4.71237311120865266379041700054847734), BOOST_MATH_BIG_CONSTANT(T, 113, -7.94125711970499027763789342500817316), BOOST_MATH_BIG_CONSTANT(T, 113, -5.74657746697664735258222071695644535), BOOST_MATH_BIG_CONSTANT(T, 113, -0.404213349456398905981223965160595687), BOOST_MATH_BIG_CONSTANT(T, 113, 2.47877781178642876561595890095758896), BOOST_MATH_BIG_CONSTANT(T, 113, 2.07714151702455125992166949812126433), BOOST_MATH_BIG_CONSTANT(T, 113, 0.858877899162360138844032265418028567), BOOST_MATH_BIG_CONSTANT(T, 113, 0.20499222604410032375789018837922397), BOOST_MATH_BIG_CONSTANT(T, 113, 0.0272103140348194747360175268778415049), BOOST_MATH_BIG_CONSTANT(T, 113, 0.0015764849020876949848954081173520686), }; static const T Q_1_2[] = { BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), BOOST_MATH_BIG_CONSTANT(T, 113, 4.71237311120863419878375031457715223), BOOST_MATH_BIG_CONSTANT(T, 113, 9.58619118655339853449127952145877467), BOOST_MATH_BIG_CONSTANT(T, 113, 11.0940067269829372437561421279054968), BOOST_MATH_BIG_CONSTANT(T, 113, 8.09075424749327792073276309969037885), BOOST_MATH_BIG_CONSTANT(T, 113, 3.87705890159891405185343806884451286), BOOST_MATH_BIG_CONSTANT(T, 113, 1.22758678701914477836330837816976782), BOOST_MATH_BIG_CONSTANT(T, 113, 0.249092040606385004109672077814668716), BOOST_MATH_BIG_CONSTANT(T, 113, 0.0295750413900655597027079600025569048), BOOST_MATH_BIG_CONSTANT(T, 113, 0.00157648490200498142247694709728858139), BOOST_MATH_BIG_CONSTANT(T, 113, 0.161264050344059471721062360645432809e-14), }; // Max error in interpolated form: 8.958e-035 static const T P_2_4[] = { BOOST_MATH_BIG_CONSTANT(T, 113, -2.55843734739907925764326773972215085), BOOST_MATH_BIG_CONSTANT(T, 113, -12.2830208240542011967952466273455887), BOOST_MATH_BIG_CONSTANT(T, 113, -23.9195022162767993526575786066414403), BOOST_MATH_BIG_CONSTANT(T, 113, -24.9256431504823483094158828285470862), BOOST_MATH_BIG_CONSTANT(T, 113, -14.7979122765478779075108064826412285), BOOST_MATH_BIG_CONSTANT(T, 113, -4.46654453928610666393276765059122272), BOOST_MATH_BIG_CONSTANT(T, 113, -0.0191439033405649675717082465687845002), BOOST_MATH_BIG_CONSTANT(T, 113, 0.515412052554351265708917209749037352), BOOST_MATH_BIG_CONSTANT(T, 113, 0.195378348786064304378247325360320038), BOOST_MATH_BIG_CONSTANT(T, 113, 0.0334761282624174313035014426794245393), BOOST_MATH_BIG_CONSTANT(T, 113, 0.002373665205942206348500250056602687), }; static const T Q_2_4[] = { BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), BOOST_MATH_BIG_CONSTANT(T, 113, 4.80098558454419907830670928248659245), BOOST_MATH_BIG_CONSTANT(T, 113, 9.99220727843170133895059300223445265), BOOST_MATH_BIG_CONSTANT(T, 113, 11.8896146167631330735386697123464976), BOOST_MATH_BIG_CONSTANT(T, 113, 8.96613256683809091593793565879092581), BOOST_MATH_BIG_CONSTANT(T, 113, 4.47254136149624110878909334574485751), BOOST_MATH_BIG_CONSTANT(T, 113, 1.48600982028196527372434773913633152), BOOST_MATH_BIG_CONSTANT(T, 113, 0.319570735766764237068541501137990078), BOOST_MATH_BIG_CONSTANT(T, 113, 0.0407358345787680953107374215319322066), BOOST_MATH_BIG_CONSTANT(T, 113, 0.00237366520593271641375755486420859837), BOOST_MATH_BIG_CONSTANT(T, 113, 0.239554887903526152679337256236302116e-15), BOOST_MATH_BIG_CONSTANT(T, 113, -0.294749244740618656265237072002026314e-17), }; static const T y_offset_2_4 = BOOST_MATH_BIG_CONSTANT(T, 113, 3.558437347412109375); // Max error in interpolated form: 4.319e-035 static const T P_4_8[] = { BOOST_MATH_BIG_CONSTANT(T, 113, 0.166626112697021464248967707021688845e-16), BOOST_MATH_BIG_CONSTANT(T, 113, 0.499999999999997739552090249208808197), BOOST_MATH_BIG_CONSTANT(T, 113, 6.40270945019053817915772473771553187), BOOST_MATH_BIG_CONSTANT(T, 113, 41.3833374155000608013677627389343329), BOOST_MATH_BIG_CONSTANT(T, 113, 166.803341854562809335667241074035245), BOOST_MATH_BIG_CONSTANT(T, 113, 453.39964786925369319960722793414521), BOOST_MATH_BIG_CONSTANT(T, 113, 851.153712317697055375935433362983944), BOOST_MATH_BIG_CONSTANT(T, 113, 1097.70657567285059133109286478004458), BOOST_MATH_BIG_CONSTANT(T, 113, 938.431232478455316020076349367632922), BOOST_MATH_BIG_CONSTANT(T, 113, 487.268001604651932322080970189930074), BOOST_MATH_BIG_CONSTANT(T, 113, 119.953445242335730062471193124820659), }; static const T Q_4_8[] = { BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), BOOST_MATH_BIG_CONSTANT(T, 113, 12.4720855670474488978638945855932398), BOOST_MATH_BIG_CONSTANT(T, 113, 78.6093129753298570701376952709727391), BOOST_MATH_BIG_CONSTANT(T, 113, 307.470246050318322489781182863190127), BOOST_MATH_BIG_CONSTANT(T, 113, 805.140686101151538537565264188630079), BOOST_MATH_BIG_CONSTANT(T, 113, 1439.12019760292146454787601409644413), BOOST_MATH_BIG_CONSTANT(T, 113, 1735.6105285756048831268586001383127), BOOST_MATH_BIG_CONSTANT(T, 113, 1348.32500712856328019355198611280536), BOOST_MATH_BIG_CONSTANT(T, 113, 607.225985860570846699704222144650563), BOOST_MATH_BIG_CONSTANT(T, 113, 119.952317857277045332558673164517227), BOOST_MATH_BIG_CONSTANT(T, 113, 0.000140165918355036060868680809129436084), }; // Maximum Deviation Found: 2.867e-035 // Expected Error Term : 2.866e-035 // Maximum Relative Change in Control Points : 2.662e-004 static const T P_8_16[] = { BOOST_MATH_BIG_CONSTANT(T, 113, -0.184828315274146610610872315609837439e-19), BOOST_MATH_BIG_CONSTANT(T, 113, 0.500000000000000004122475157735807738), BOOST_MATH_BIG_CONSTANT(T, 113, 3.02533865247313349284875558880415875), BOOST_MATH_BIG_CONSTANT(T, 113, 13.5995927517457371243039532492642734), BOOST_MATH_BIG_CONSTANT(T, 113, 35.3132224283087906757037999452941588), BOOST_MATH_BIG_CONSTANT(T, 113, 67.1639424550714159157603179911505619), BOOST_MATH_BIG_CONSTANT(T, 113, 83.5767733658513967581959839367419891), BOOST_MATH_BIG_CONSTANT(T, 113, 71.073491212235705900866411319363501), BOOST_MATH_BIG_CONSTANT(T, 113, 35.8621515614725564575893663483998663), BOOST_MATH_BIG_CONSTANT(T, 113, 8.72152231639983491987779743154333318), }; static const T Q_8_16[] = { BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), BOOST_MATH_BIG_CONSTANT(T, 113, 5.71734397161293452310624822415866372), BOOST_MATH_BIG_CONSTANT(T, 113, 25.293404179620438179337103263274815), BOOST_MATH_BIG_CONSTANT(T, 113, 62.2619767967468199111077640625328469), BOOST_MATH_BIG_CONSTANT(T, 113, 113.955048909238993473389714972250235), BOOST_MATH_BIG_CONSTANT(T, 113, 130.807138328938966981862203944329408), BOOST_MATH_BIG_CONSTANT(T, 113, 102.423146902337654110717764213057753), BOOST_MATH_BIG_CONSTANT(T, 113, 44.0424772805245202514468199602123565), BOOST_MATH_BIG_CONSTANT(T, 113, 8.89898032477904072082994913461386099), BOOST_MATH_BIG_CONSTANT(T, 113, -0.0296627336872039988632793863671456398), }; // Maximum Deviation Found: 1.079e-035 // Expected Error Term : -1.079e-035 // Maximum Relative Change in Control Points : 7.884e-003 static const T P_16_inf[] = { BOOST_MATH_BIG_CONSTANT(T, 113, 0.0), BOOST_MATH_BIG_CONSTANT(T, 113, 0.500000000000000000000000000000087317), BOOST_MATH_BIG_CONSTANT(T, 113, 0.345625669885456215194494735902663968), BOOST_MATH_BIG_CONSTANT(T, 113, 9.62895499360842232127552650044647769), BOOST_MATH_BIG_CONSTANT(T, 113, 3.5936085382439026269301003761320812), BOOST_MATH_BIG_CONSTANT(T, 113, 49.459599118438883265036646019410669), BOOST_MATH_BIG_CONSTANT(T, 113, 7.77519237321893917784735690560496607), BOOST_MATH_BIG_CONSTANT(T, 113, 74.4536074488178075948642351179304121), BOOST_MATH_BIG_CONSTANT(T, 113, 2.75209340397069050436806159297952699), BOOST_MATH_BIG_CONSTANT(T, 113, 23.9292359711471667884504840186561598), }; static const T Q_16_inf[] = { BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), BOOST_MATH_BIG_CONSTANT(T, 113, 0.357918006437579097055656138920742037), BOOST_MATH_BIG_CONSTANT(T, 113, 19.1386039850709849435325005484512944), BOOST_MATH_BIG_CONSTANT(T, 113, 0.874349081464143606016221431763364517), BOOST_MATH_BIG_CONSTANT(T, 113, 98.6516097434855572678195488061432509), BOOST_MATH_BIG_CONSTANT(T, 113, -16.1051972833382893468655223662534306), BOOST_MATH_BIG_CONSTANT(T, 113, 154.316860216253720989145047141653727), BOOST_MATH_BIG_CONSTANT(T, 113, -40.2026880424378986053105969312264534), BOOST_MATH_BIG_CONSTANT(T, 113, 60.1679136674264778074736441126810223), BOOST_MATH_BIG_CONSTANT(T, 113, -13.3414844622256422644504472438320114), BOOST_MATH_BIG_CONSTANT(T, 113, 2.53795636200649908779512969030363442), }; if(x <= 2) { return (2 + boost::math::tools::evaluate_polynomial(P_1_2, x) / tools::evaluate_polynomial(Q_1_2, x)) / (x * x); } else if(x <= 4) { return (y_offset_2_4 + boost::math::tools::evaluate_polynomial(P_2_4, x) / tools::evaluate_polynomial(Q_2_4, x)) / (x * x); } else if(x <= 8) { T y = 1 / x; return (1 + tools::evaluate_polynomial(P_4_8, y) / tools::evaluate_polynomial(Q_4_8, y)) / x; } else if(x <= 16) { T y = 1 / x; return (1 + tools::evaluate_polynomial(P_8_16, y) / tools::evaluate_polynomial(Q_8_16, y)) / x; } T y = 1 / x; return (1 + tools::evaluate_polynomial(P_16_inf, y) / tools::evaluate_polynomial(Q_16_inf, y)) / x; } template <class T, class Tag, class Policy> T trigamma_imp(T x, const Tag* t, const Policy& pol) { // // This handles reflection of negative arguments, and all our // error handling, then forwards to the T-specific approximation. // BOOST_MATH_STD_USING // ADL of std functions. T result = 0; // // Check for negative arguments and use reflection: // if(x <= 0) { // Reflect: T z = 1 - x; // Argument reduction for tan: if(floor(x) == x) { return policies::raise_pole_error<T>("boost::math::trigamma<%1%>(%1%)", 0, (1-x), pol); } T s = fabs(x) < fabs(z) ? boost::math::sin_pi(x, pol) : boost::math::sin_pi(z, pol); return -trigamma_imp(z, t, pol) + boost::math::pow<2>(constants::pi<T>()) / (s * s); } if(x < 1) { result = 1 / (x * x); x += 1; } return result + trigamma_prec(x, t, pol); } template <class T, class Policy> T trigamma_imp(T x, const std::integral_constant<int, 0>*, const Policy& pol) { return polygamma_imp(1, x, pol); } // // Initializer: ensure all our constants are initialized prior to the first call of main: // template <class T, class Policy> struct trigamma_initializer { struct init { init() { typedef typename policies::precision<T, Policy>::type precision_type; do_init(std::integral_constant<bool, precision_type::value && (precision_type::value <= 113)>()); } void do_init(const std::true_type&) { boost::math::trigamma(T(2.5), Policy()); } void do_init(const std::false_type&){} void force_instantiate()const{} }; static const init initializer; static void force_instantiate() { initializer.force_instantiate(); } }; template <class T, class Policy> const typename trigamma_initializer<T, Policy>::init trigamma_initializer<T, Policy>::initializer; } // namespace detail template <class T, class Policy> inline typename tools::promote_args<T>::type trigamma(T x, const Policy&) { typedef typename tools::promote_args<T>::type result_type; typedef typename policies::evaluation<result_type, Policy>::type value_type; typedef typename policies::precision<T, Policy>::type precision_type; typedef std::integral_constant<int, precision_type::value <= 0 ? 0 : precision_type::value <= 53 ? 53 : precision_type::value <= 64 ? 64 : precision_type::value <= 113 ? 113 : 0 > tag_type; typedef typename policies::normalise< Policy, policies::promote_float<false>, policies::promote_double<false>, policies::discrete_quantile<>, policies::assert_undefined<> >::type forwarding_policy; // Force initialization of constants: detail::trigamma_initializer<value_type, forwarding_policy>::force_instantiate(); return policies::checked_narrowing_cast<result_type, Policy>(detail::trigamma_imp( static_cast<value_type>(x), static_cast<const tag_type*>(0), forwarding_policy()), "boost::math::trigamma<%1%>(%1%)"); } template <class T> inline typename tools::promote_args<T>::type trigamma(T x) { return trigamma(x, policies::policy<>()); } } // namespace math } // namespace boost #endif