1 // (C) Copyright John Maddock 2006. 2 // Use, modification and distribution are subject to the 3 // Boost Software License, Version 1.0. (See accompanying file 4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) 5 6 #ifndef BOOST_MATH_SF_TRIGAMMA_HPP 7 #define BOOST_MATH_SF_TRIGAMMA_HPP 8 9 #ifdef _MSC_VER 10 #pragma once 11 #endif 12 13 #include <boost/math/special_functions/math_fwd.hpp> 14 #include <boost/math/tools/rational.hpp> 15 #include <boost/math/tools/series.hpp> 16 #include <boost/math/tools/promotion.hpp> 17 #include <boost/math/policies/error_handling.hpp> 18 #include <boost/math/constants/constants.hpp> 19 #include <boost/math/tools/big_constant.hpp> 20 #include <boost/math/special_functions/polygamma.hpp> 21 22 #if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128) 23 // 24 // This is the only way we can avoid 25 // warning: non-standard suffix on floating constant [-Wpedantic] 26 // when building with -Wall -pedantic. Neither __extension__ 27 // nor #pragma diagnostic ignored work :( 28 // 29 #pragma GCC system_header 30 #endif 31 32 namespace boost{ 33 namespace math{ 34 namespace detail{ 35 36 template<class T, class Policy> 37 T polygamma_imp(const int n, T x, const Policy &pol); 38 39 template <class T, class Policy> 40 T trigamma_prec(T x, const std::integral_constant<int, 53>*, const Policy&) 41 { 42 // Max error in interpolated form: 3.736e-017 43 static const T offset = BOOST_MATH_BIG_CONSTANT(T, 53, 2.1093254089355469); 44 static const T P_1_2[] = { 45 BOOST_MATH_BIG_CONSTANT(T, 53, -1.1093280605946045), 46 BOOST_MATH_BIG_CONSTANT(T, 53, -3.8310674472619321), 47 BOOST_MATH_BIG_CONSTANT(T, 53, -3.3703848401898283), 48 BOOST_MATH_BIG_CONSTANT(T, 53, 0.28080574467981213), 49 BOOST_MATH_BIG_CONSTANT(T, 53, 1.6638069578676164), 50 BOOST_MATH_BIG_CONSTANT(T, 53, 0.64468386819102836), 51 }; 52 static const T Q_1_2[] = { 53 BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), 54 BOOST_MATH_BIG_CONSTANT(T, 53, 3.4535389668541151), 55 BOOST_MATH_BIG_CONSTANT(T, 53, 4.5208926987851437), 56 BOOST_MATH_BIG_CONSTANT(T, 53, 2.7012734178351534), 57 BOOST_MATH_BIG_CONSTANT(T, 53, 0.64468798399785611), 58 BOOST_MATH_BIG_CONSTANT(T, 53, -0.20314516859987728e-6), 59 }; 60 // Max error in interpolated form: 1.159e-017 61 static const T P_2_4[] = { 62 BOOST_MATH_BIG_CONSTANT(T, 53, -0.13803835004508849e-7), 63 BOOST_MATH_BIG_CONSTANT(T, 53, 0.50000049158540261), 64 BOOST_MATH_BIG_CONSTANT(T, 53, 1.6077979838469348), 65 BOOST_MATH_BIG_CONSTANT(T, 53, 2.5645435828098254), 66 BOOST_MATH_BIG_CONSTANT(T, 53, 2.0534873203680393), 67 BOOST_MATH_BIG_CONSTANT(T, 53, 0.74566981111565923), 68 }; 69 static const T Q_2_4[] = { 70 BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), 71 BOOST_MATH_BIG_CONSTANT(T, 53, 2.8822787662376169), 72 BOOST_MATH_BIG_CONSTANT(T, 53, 4.1681660554090917), 73 BOOST_MATH_BIG_CONSTANT(T, 53, 2.7853527819234466), 74 BOOST_MATH_BIG_CONSTANT(T, 53, 0.74967671848044792), 75 BOOST_MATH_BIG_CONSTANT(T, 53, -0.00057069112416246805), 76 }; 77 // Maximum Deviation Found: 6.896e-018 78 // Expected Error Term : -6.895e-018 79 // Maximum Relative Change in Control Points : 8.497e-004 80 static const T P_4_inf[] = { 81 static_cast<T>(0.68947581948701249e-17L), 82 static_cast<T>(0.49999999999998975L), 83 static_cast<T>(1.0177274392923795L), 84 static_cast<T>(2.498208511343429L), 85 static_cast<T>(2.1921221359427595L), 86 static_cast<T>(1.5897035272532764L), 87 static_cast<T>(0.40154388356961734L), 88 }; 89 static const T Q_4_inf[] = { 90 static_cast<T>(1.0L), 91 static_cast<T>(1.7021215452463932L), 92 static_cast<T>(4.4290431747556469L), 93 static_cast<T>(2.9745631894384922L), 94 static_cast<T>(2.3013614809773616L), 95 static_cast<T>(0.28360399799075752L), 96 static_cast<T>(0.022892987908906897L), 97 }; 98 99 if(x <= 2) 100 { 101 return (offset + boost::math::tools::evaluate_polynomial(P_1_2, x) / tools::evaluate_polynomial(Q_1_2, x)) / (x * x); 102 } 103 else if(x <= 4) 104 { 105 T y = 1 / x; 106 return (1 + tools::evaluate_polynomial(P_2_4, y) / tools::evaluate_polynomial(Q_2_4, y)) / x; 107 } 108 T y = 1 / x; 109 return (1 + tools::evaluate_polynomial(P_4_inf, y) / tools::evaluate_polynomial(Q_4_inf, y)) / x; 110 } 111 112 template <class T, class Policy> 113 T trigamma_prec(T x, const std::integral_constant<int, 64>*, const Policy&) 114 { 115 // Max error in interpolated form: 1.178e-020 116 static const T offset_1_2 = BOOST_MATH_BIG_CONSTANT(T, 64, 2.109325408935546875); 117 static const T P_1_2[] = { 118 BOOST_MATH_BIG_CONSTANT(T, 64, -1.10932535608960258341), 119 BOOST_MATH_BIG_CONSTANT(T, 64, -4.18793841543017129052), 120 BOOST_MATH_BIG_CONSTANT(T, 64, -4.63865531898487734531), 121 BOOST_MATH_BIG_CONSTANT(T, 64, -0.919832884430500908047), 122 BOOST_MATH_BIG_CONSTANT(T, 64, 1.68074038333180423012), 123 BOOST_MATH_BIG_CONSTANT(T, 64, 1.21172611429185622377), 124 BOOST_MATH_BIG_CONSTANT(T, 64, 0.259635673503366427284), 125 }; 126 static const T Q_1_2[] = { 127 BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), 128 BOOST_MATH_BIG_CONSTANT(T, 64, 3.77521119359546982995), 129 BOOST_MATH_BIG_CONSTANT(T, 64, 5.664338024578956321), 130 BOOST_MATH_BIG_CONSTANT(T, 64, 4.25995134879278028361), 131 BOOST_MATH_BIG_CONSTANT(T, 64, 1.62956638448940402182), 132 BOOST_MATH_BIG_CONSTANT(T, 64, 0.259635512844691089868), 133 BOOST_MATH_BIG_CONSTANT(T, 64, 0.629642219810618032207e-8), 134 }; 135 // Max error in interpolated form: 3.912e-020 136 static const T P_2_8[] = { 137 BOOST_MATH_BIG_CONSTANT(T, 64, -0.387540035162952880976e-11), 138 BOOST_MATH_BIG_CONSTANT(T, 64, 0.500000000276430504), 139 BOOST_MATH_BIG_CONSTANT(T, 64, 3.21926880986360957306), 140 BOOST_MATH_BIG_CONSTANT(T, 64, 10.2550347708483445775), 141 BOOST_MATH_BIG_CONSTANT(T, 64, 18.9002075150709144043), 142 BOOST_MATH_BIG_CONSTANT(T, 64, 21.0357215832399705625), 143 BOOST_MATH_BIG_CONSTANT(T, 64, 13.4346512182925923978), 144 BOOST_MATH_BIG_CONSTANT(T, 64, 3.98656291026448279118), 145 }; 146 static const T Q_2_8[] = { 147 BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), 148 BOOST_MATH_BIG_CONSTANT(T, 64, 6.10520430478613667724), 149 BOOST_MATH_BIG_CONSTANT(T, 64, 18.475001060603645512), 150 BOOST_MATH_BIG_CONSTANT(T, 64, 31.7087534567758405638), 151 BOOST_MATH_BIG_CONSTANT(T, 64, 31.908814523890465398), 152 BOOST_MATH_BIG_CONSTANT(T, 64, 17.4175479039227084798), 153 BOOST_MATH_BIG_CONSTANT(T, 64, 3.98749106958394941276), 154 BOOST_MATH_BIG_CONSTANT(T, 64, -0.000115917322224411128566), 155 }; 156 // Maximum Deviation Found: 2.635e-020 157 // Expected Error Term : 2.635e-020 158 // Maximum Relative Change in Control Points : 1.791e-003 159 static const T P_8_inf[] = { 160 BOOST_MATH_BIG_CONSTANT(T, 64, -0.263527875092466899848e-19), 161 BOOST_MATH_BIG_CONSTANT(T, 64, 0.500000000000000058145), 162 BOOST_MATH_BIG_CONSTANT(T, 64, 0.0730121433777364138677), 163 BOOST_MATH_BIG_CONSTANT(T, 64, 1.94505878379957149534), 164 BOOST_MATH_BIG_CONSTANT(T, 64, 0.0517092358874932620529), 165 BOOST_MATH_BIG_CONSTANT(T, 64, 1.07995383547483921121), 166 }; 167 static const T Q_8_inf[] = { 168 BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), 169 BOOST_MATH_BIG_CONSTANT(T, 64, -0.187309046577818095504), 170 BOOST_MATH_BIG_CONSTANT(T, 64, 3.95255391645238842975), 171 BOOST_MATH_BIG_CONSTANT(T, 64, -1.14743283327078949087), 172 BOOST_MATH_BIG_CONSTANT(T, 64, 2.52989799376344914499), 173 BOOST_MATH_BIG_CONSTANT(T, 64, -0.627414303172402506396), 174 BOOST_MATH_BIG_CONSTANT(T, 64, 0.141554248216425512536), 175 }; 176 177 if(x <= 2) 178 { 179 return (offset_1_2 + boost::math::tools::evaluate_polynomial(P_1_2, x) / tools::evaluate_polynomial(Q_1_2, x)) / (x * x); 180 } 181 else if(x <= 8) 182 { 183 T y = 1 / x; 184 return (1 + tools::evaluate_polynomial(P_2_8, y) / tools::evaluate_polynomial(Q_2_8, y)) / x; 185 } 186 T y = 1 / x; 187 return (1 + tools::evaluate_polynomial(P_8_inf, y) / tools::evaluate_polynomial(Q_8_inf, y)) / x; 188 } 189 190 template <class T, class Policy> 191 T trigamma_prec(T x, const std::integral_constant<int, 113>*, const Policy&) 192 { 193 // Max error in interpolated form: 1.916e-035 194 195 static const T P_1_2[] = { 196 BOOST_MATH_BIG_CONSTANT(T, 113, -0.999999999999999082554457936871832533), 197 BOOST_MATH_BIG_CONSTANT(T, 113, -4.71237311120865266379041700054847734), 198 BOOST_MATH_BIG_CONSTANT(T, 113, -7.94125711970499027763789342500817316), 199 BOOST_MATH_BIG_CONSTANT(T, 113, -5.74657746697664735258222071695644535), 200 BOOST_MATH_BIG_CONSTANT(T, 113, -0.404213349456398905981223965160595687), 201 BOOST_MATH_BIG_CONSTANT(T, 113, 2.47877781178642876561595890095758896), 202 BOOST_MATH_BIG_CONSTANT(T, 113, 2.07714151702455125992166949812126433), 203 BOOST_MATH_BIG_CONSTANT(T, 113, 0.858877899162360138844032265418028567), 204 BOOST_MATH_BIG_CONSTANT(T, 113, 0.20499222604410032375789018837922397), 205 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0272103140348194747360175268778415049), 206 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0015764849020876949848954081173520686), 207 }; 208 static const T Q_1_2[] = { 209 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 210 BOOST_MATH_BIG_CONSTANT(T, 113, 4.71237311120863419878375031457715223), 211 BOOST_MATH_BIG_CONSTANT(T, 113, 9.58619118655339853449127952145877467), 212 BOOST_MATH_BIG_CONSTANT(T, 113, 11.0940067269829372437561421279054968), 213 BOOST_MATH_BIG_CONSTANT(T, 113, 8.09075424749327792073276309969037885), 214 BOOST_MATH_BIG_CONSTANT(T, 113, 3.87705890159891405185343806884451286), 215 BOOST_MATH_BIG_CONSTANT(T, 113, 1.22758678701914477836330837816976782), 216 BOOST_MATH_BIG_CONSTANT(T, 113, 0.249092040606385004109672077814668716), 217 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0295750413900655597027079600025569048), 218 BOOST_MATH_BIG_CONSTANT(T, 113, 0.00157648490200498142247694709728858139), 219 BOOST_MATH_BIG_CONSTANT(T, 113, 0.161264050344059471721062360645432809e-14), 220 }; 221 222 // Max error in interpolated form: 8.958e-035 223 static const T P_2_4[] = { 224 BOOST_MATH_BIG_CONSTANT(T, 113, -2.55843734739907925764326773972215085), 225 BOOST_MATH_BIG_CONSTANT(T, 113, -12.2830208240542011967952466273455887), 226 BOOST_MATH_BIG_CONSTANT(T, 113, -23.9195022162767993526575786066414403), 227 BOOST_MATH_BIG_CONSTANT(T, 113, -24.9256431504823483094158828285470862), 228 BOOST_MATH_BIG_CONSTANT(T, 113, -14.7979122765478779075108064826412285), 229 BOOST_MATH_BIG_CONSTANT(T, 113, -4.46654453928610666393276765059122272), 230 BOOST_MATH_BIG_CONSTANT(T, 113, -0.0191439033405649675717082465687845002), 231 BOOST_MATH_BIG_CONSTANT(T, 113, 0.515412052554351265708917209749037352), 232 BOOST_MATH_BIG_CONSTANT(T, 113, 0.195378348786064304378247325360320038), 233 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0334761282624174313035014426794245393), 234 BOOST_MATH_BIG_CONSTANT(T, 113, 0.002373665205942206348500250056602687), 235 }; 236 static const T Q_2_4[] = { 237 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 238 BOOST_MATH_BIG_CONSTANT(T, 113, 4.80098558454419907830670928248659245), 239 BOOST_MATH_BIG_CONSTANT(T, 113, 9.99220727843170133895059300223445265), 240 BOOST_MATH_BIG_CONSTANT(T, 113, 11.8896146167631330735386697123464976), 241 BOOST_MATH_BIG_CONSTANT(T, 113, 8.96613256683809091593793565879092581), 242 BOOST_MATH_BIG_CONSTANT(T, 113, 4.47254136149624110878909334574485751), 243 BOOST_MATH_BIG_CONSTANT(T, 113, 1.48600982028196527372434773913633152), 244 BOOST_MATH_BIG_CONSTANT(T, 113, 0.319570735766764237068541501137990078), 245 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0407358345787680953107374215319322066), 246 BOOST_MATH_BIG_CONSTANT(T, 113, 0.00237366520593271641375755486420859837), 247 BOOST_MATH_BIG_CONSTANT(T, 113, 0.239554887903526152679337256236302116e-15), 248 BOOST_MATH_BIG_CONSTANT(T, 113, -0.294749244740618656265237072002026314e-17), 249 }; 250 251 static const T y_offset_2_4 = BOOST_MATH_BIG_CONSTANT(T, 113, 3.558437347412109375); 252 253 // Max error in interpolated form: 4.319e-035 254 static const T P_4_8[] = { 255 BOOST_MATH_BIG_CONSTANT(T, 113, 0.166626112697021464248967707021688845e-16), 256 BOOST_MATH_BIG_CONSTANT(T, 113, 0.499999999999997739552090249208808197), 257 BOOST_MATH_BIG_CONSTANT(T, 113, 6.40270945019053817915772473771553187), 258 BOOST_MATH_BIG_CONSTANT(T, 113, 41.3833374155000608013677627389343329), 259 BOOST_MATH_BIG_CONSTANT(T, 113, 166.803341854562809335667241074035245), 260 BOOST_MATH_BIG_CONSTANT(T, 113, 453.39964786925369319960722793414521), 261 BOOST_MATH_BIG_CONSTANT(T, 113, 851.153712317697055375935433362983944), 262 BOOST_MATH_BIG_CONSTANT(T, 113, 1097.70657567285059133109286478004458), 263 BOOST_MATH_BIG_CONSTANT(T, 113, 938.431232478455316020076349367632922), 264 BOOST_MATH_BIG_CONSTANT(T, 113, 487.268001604651932322080970189930074), 265 BOOST_MATH_BIG_CONSTANT(T, 113, 119.953445242335730062471193124820659), 266 }; 267 static const T Q_4_8[] = { 268 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 269 BOOST_MATH_BIG_CONSTANT(T, 113, 12.4720855670474488978638945855932398), 270 BOOST_MATH_BIG_CONSTANT(T, 113, 78.6093129753298570701376952709727391), 271 BOOST_MATH_BIG_CONSTANT(T, 113, 307.470246050318322489781182863190127), 272 BOOST_MATH_BIG_CONSTANT(T, 113, 805.140686101151538537565264188630079), 273 BOOST_MATH_BIG_CONSTANT(T, 113, 1439.12019760292146454787601409644413), 274 BOOST_MATH_BIG_CONSTANT(T, 113, 1735.6105285756048831268586001383127), 275 BOOST_MATH_BIG_CONSTANT(T, 113, 1348.32500712856328019355198611280536), 276 BOOST_MATH_BIG_CONSTANT(T, 113, 607.225985860570846699704222144650563), 277 BOOST_MATH_BIG_CONSTANT(T, 113, 119.952317857277045332558673164517227), 278 BOOST_MATH_BIG_CONSTANT(T, 113, 0.000140165918355036060868680809129436084), 279 }; 280 281 // Maximum Deviation Found: 2.867e-035 282 // Expected Error Term : 2.866e-035 283 // Maximum Relative Change in Control Points : 2.662e-004 284 static const T P_8_16[] = { 285 BOOST_MATH_BIG_CONSTANT(T, 113, -0.184828315274146610610872315609837439e-19), 286 BOOST_MATH_BIG_CONSTANT(T, 113, 0.500000000000000004122475157735807738), 287 BOOST_MATH_BIG_CONSTANT(T, 113, 3.02533865247313349284875558880415875), 288 BOOST_MATH_BIG_CONSTANT(T, 113, 13.5995927517457371243039532492642734), 289 BOOST_MATH_BIG_CONSTANT(T, 113, 35.3132224283087906757037999452941588), 290 BOOST_MATH_BIG_CONSTANT(T, 113, 67.1639424550714159157603179911505619), 291 BOOST_MATH_BIG_CONSTANT(T, 113, 83.5767733658513967581959839367419891), 292 BOOST_MATH_BIG_CONSTANT(T, 113, 71.073491212235705900866411319363501), 293 BOOST_MATH_BIG_CONSTANT(T, 113, 35.8621515614725564575893663483998663), 294 BOOST_MATH_BIG_CONSTANT(T, 113, 8.72152231639983491987779743154333318), 295 }; 296 static const T Q_8_16[] = { 297 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 298 BOOST_MATH_BIG_CONSTANT(T, 113, 5.71734397161293452310624822415866372), 299 BOOST_MATH_BIG_CONSTANT(T, 113, 25.293404179620438179337103263274815), 300 BOOST_MATH_BIG_CONSTANT(T, 113, 62.2619767967468199111077640625328469), 301 BOOST_MATH_BIG_CONSTANT(T, 113, 113.955048909238993473389714972250235), 302 BOOST_MATH_BIG_CONSTANT(T, 113, 130.807138328938966981862203944329408), 303 BOOST_MATH_BIG_CONSTANT(T, 113, 102.423146902337654110717764213057753), 304 BOOST_MATH_BIG_CONSTANT(T, 113, 44.0424772805245202514468199602123565), 305 BOOST_MATH_BIG_CONSTANT(T, 113, 8.89898032477904072082994913461386099), 306 BOOST_MATH_BIG_CONSTANT(T, 113, -0.0296627336872039988632793863671456398), 307 }; 308 // Maximum Deviation Found: 1.079e-035 309 // Expected Error Term : -1.079e-035 310 // Maximum Relative Change in Control Points : 7.884e-003 311 static const T P_16_inf[] = { 312 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0), 313 BOOST_MATH_BIG_CONSTANT(T, 113, 0.500000000000000000000000000000087317), 314 BOOST_MATH_BIG_CONSTANT(T, 113, 0.345625669885456215194494735902663968), 315 BOOST_MATH_BIG_CONSTANT(T, 113, 9.62895499360842232127552650044647769), 316 BOOST_MATH_BIG_CONSTANT(T, 113, 3.5936085382439026269301003761320812), 317 BOOST_MATH_BIG_CONSTANT(T, 113, 49.459599118438883265036646019410669), 318 BOOST_MATH_BIG_CONSTANT(T, 113, 7.77519237321893917784735690560496607), 319 BOOST_MATH_BIG_CONSTANT(T, 113, 74.4536074488178075948642351179304121), 320 BOOST_MATH_BIG_CONSTANT(T, 113, 2.75209340397069050436806159297952699), 321 BOOST_MATH_BIG_CONSTANT(T, 113, 23.9292359711471667884504840186561598), 322 }; 323 static const T Q_16_inf[] = { 324 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 325 BOOST_MATH_BIG_CONSTANT(T, 113, 0.357918006437579097055656138920742037), 326 BOOST_MATH_BIG_CONSTANT(T, 113, 19.1386039850709849435325005484512944), 327 BOOST_MATH_BIG_CONSTANT(T, 113, 0.874349081464143606016221431763364517), 328 BOOST_MATH_BIG_CONSTANT(T, 113, 98.6516097434855572678195488061432509), 329 BOOST_MATH_BIG_CONSTANT(T, 113, -16.1051972833382893468655223662534306), 330 BOOST_MATH_BIG_CONSTANT(T, 113, 154.316860216253720989145047141653727), 331 BOOST_MATH_BIG_CONSTANT(T, 113, -40.2026880424378986053105969312264534), 332 BOOST_MATH_BIG_CONSTANT(T, 113, 60.1679136674264778074736441126810223), 333 BOOST_MATH_BIG_CONSTANT(T, 113, -13.3414844622256422644504472438320114), 334 BOOST_MATH_BIG_CONSTANT(T, 113, 2.53795636200649908779512969030363442), 335 }; 336 337 if(x <= 2) 338 { 339 return (2 + boost::math::tools::evaluate_polynomial(P_1_2, x) / tools::evaluate_polynomial(Q_1_2, x)) / (x * x); 340 } 341 else if(x <= 4) 342 { 343 return (y_offset_2_4 + boost::math::tools::evaluate_polynomial(P_2_4, x) / tools::evaluate_polynomial(Q_2_4, x)) / (x * x); 344 } 345 else if(x <= 8) 346 { 347 T y = 1 / x; 348 return (1 + tools::evaluate_polynomial(P_4_8, y) / tools::evaluate_polynomial(Q_4_8, y)) / x; 349 } 350 else if(x <= 16) 351 { 352 T y = 1 / x; 353 return (1 + tools::evaluate_polynomial(P_8_16, y) / tools::evaluate_polynomial(Q_8_16, y)) / x; 354 } 355 T y = 1 / x; 356 return (1 + tools::evaluate_polynomial(P_16_inf, y) / tools::evaluate_polynomial(Q_16_inf, y)) / x; 357 } 358 359 template <class T, class Tag, class Policy> 360 T trigamma_imp(T x, const Tag* t, const Policy& pol) 361 { 362 // 363 // This handles reflection of negative arguments, and all our 364 // error handling, then forwards to the T-specific approximation. 365 // 366 BOOST_MATH_STD_USING // ADL of std functions. 367 368 T result = 0; 369 // 370 // Check for negative arguments and use reflection: 371 // 372 if(x <= 0) 373 { 374 // Reflect: 375 T z = 1 - x; 376 // Argument reduction for tan: 377 if(floor(x) == x) 378 { 379 return policies::raise_pole_error<T>("boost::math::trigamma<%1%>(%1%)", 0, (1-x), pol); 380 } 381 T s = fabs(x) < fabs(z) ? boost::math::sin_pi(x, pol) : boost::math::sin_pi(z, pol); 382 return -trigamma_imp(z, t, pol) + boost::math::pow<2>(constants::pi<T>()) / (s * s); 383 } 384 if(x < 1) 385 { 386 result = 1 / (x * x); 387 x += 1; 388 } 389 return result + trigamma_prec(x, t, pol); 390 } 391 392 template <class T, class Policy> 393 T trigamma_imp(T x, const std::integral_constant<int, 0>*, const Policy& pol) 394 { 395 return polygamma_imp(1, x, pol); 396 } 397 // 398 // Initializer: ensure all our constants are initialized prior to the first call of main: 399 // 400 template <class T, class Policy> 401 struct trigamma_initializer 402 { 403 struct init 404 { initboost::math::detail::trigamma_initializer::init405 init() 406 { 407 typedef typename policies::precision<T, Policy>::type precision_type; 408 do_init(std::integral_constant<bool, precision_type::value && (precision_type::value <= 113)>()); 409 } do_initboost::math::detail::trigamma_initializer::init410 void do_init(const std::true_type&) 411 { 412 boost::math::trigamma(T(2.5), Policy()); 413 } do_initboost::math::detail::trigamma_initializer::init414 void do_init(const std::false_type&){} force_instantiateboost::math::detail::trigamma_initializer::init415 void force_instantiate()const{} 416 }; 417 static const init initializer; force_instantiateboost::math::detail::trigamma_initializer418 static void force_instantiate() 419 { 420 initializer.force_instantiate(); 421 } 422 }; 423 424 template <class T, class Policy> 425 const typename trigamma_initializer<T, Policy>::init trigamma_initializer<T, Policy>::initializer; 426 427 } // namespace detail 428 429 template <class T, class Policy> 430 inline typename tools::promote_args<T>::type trigamma(T x,const Policy &)431 trigamma(T x, const Policy&) 432 { 433 typedef typename tools::promote_args<T>::type result_type; 434 typedef typename policies::evaluation<result_type, Policy>::type value_type; 435 typedef typename policies::precision<T, Policy>::type precision_type; 436 typedef std::integral_constant<int, 437 precision_type::value <= 0 ? 0 : 438 precision_type::value <= 53 ? 53 : 439 precision_type::value <= 64 ? 64 : 440 precision_type::value <= 113 ? 113 : 0 441 > tag_type; 442 typedef typename policies::normalise< 443 Policy, 444 policies::promote_float<false>, 445 policies::promote_double<false>, 446 policies::discrete_quantile<>, 447 policies::assert_undefined<> >::type forwarding_policy; 448 449 // Force initialization of constants: 450 detail::trigamma_initializer<value_type, forwarding_policy>::force_instantiate(); 451 452 return policies::checked_narrowing_cast<result_type, Policy>(detail::trigamma_imp( 453 static_cast<value_type>(x), 454 static_cast<const tag_type*>(0), forwarding_policy()), "boost::math::trigamma<%1%>(%1%)"); 455 } 456 457 template <class T> 458 inline typename tools::promote_args<T>::type trigamma(T x)459 trigamma(T x) 460 { 461 return trigamma(x, policies::policy<>()); 462 } 463 464 } // namespace math 465 } // namespace boost 466 #endif 467 468