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+++ b/boost/math/special_functions/trigamma.hpp
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+// (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/mpl/comparison.hpp>
+#include <boost/math/tools/big_constant.hpp>
+#include <boost/math/special_functions/polygamma.hpp>
+
+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 mpl::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[] = {
+ 0.68947581948701249e-17L,
+ 0.49999999999998975L,
+ 1.0177274392923795L,
+ 2.498208511343429L,
+ 2.1921221359427595L,
+ 1.5897035272532764L,
+ 0.40154388356961734L,
+ };
+ static const T Q_4_inf[] = {
+ 1.0L,
+ 1.7021215452463932L,
+ 4.4290431747556469L,
+ 2.9745631894384922L,
+ 2.3013614809773616L,
+ 0.28360399799075752L,
+ 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 mpl::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 mpl::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 mpl::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(mpl::bool_<precision_type::value && (precision_type::value <= 113)>());
+ }
+ void do_init(const mpl::true_&)
+ {
+ boost::math::trigamma(T(2.5), Policy());
+ }
+ void do_init(const mpl::false_&){}
+ 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 typename mpl::if_<
+ mpl::or_<
+ mpl::less_equal<precision_type, mpl::int_<0> >,
+ mpl::greater<precision_type, mpl::int_<114> >
+ >,
+ mpl::int_<0>,
+ typename mpl::if_<
+ mpl::less<precision_type, mpl::int_<54> >,
+ mpl::int_<53>,
+ typename mpl::if_<
+ mpl::less<precision_type, mpl::int_<65> >,
+ mpl::int_<64>,
+ mpl::int_<113>
+ >::type
+ >::type
+ >::type 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
+