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/mpl/comparison.hpp> 20 #include <boost/math/tools/big_constant.hpp> 21 #include <boost/math/special_functions/polygamma.hpp> 22 23 namespace boost{ 24 namespace math{ 25 namespace detail{ 26 27 template<class T, class Policy> 28 T polygamma_imp(const int n, T x, const Policy &pol); 29 30 template <class T, class Policy> 31 T trigamma_prec(T x, const mpl::int_<53>*, const Policy&) 32 { 33 // Max error in interpolated form: 3.736e-017 34 static const T offset = BOOST_MATH_BIG_CONSTANT(T, 53, 2.1093254089355469); 35 static const T P_1_2[] = { 36 BOOST_MATH_BIG_CONSTANT(T, 53, -1.1093280605946045), 37 BOOST_MATH_BIG_CONSTANT(T, 53, -3.8310674472619321), 38 BOOST_MATH_BIG_CONSTANT(T, 53, -3.3703848401898283), 39 BOOST_MATH_BIG_CONSTANT(T, 53, 0.28080574467981213), 40 BOOST_MATH_BIG_CONSTANT(T, 53, 1.6638069578676164), 41 BOOST_MATH_BIG_CONSTANT(T, 53, 0.64468386819102836), 42 }; 43 static const T Q_1_2[] = { 44 BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), 45 BOOST_MATH_BIG_CONSTANT(T, 53, 3.4535389668541151), 46 BOOST_MATH_BIG_CONSTANT(T, 53, 4.5208926987851437), 47 BOOST_MATH_BIG_CONSTANT(T, 53, 2.7012734178351534), 48 BOOST_MATH_BIG_CONSTANT(T, 53, 0.64468798399785611), 49 BOOST_MATH_BIG_CONSTANT(T, 53, -0.20314516859987728e-6), 50 }; 51 // Max error in interpolated form: 1.159e-017 52 static const T P_2_4[] = { 53 BOOST_MATH_BIG_CONSTANT(T, 53, -0.13803835004508849e-7), 54 BOOST_MATH_BIG_CONSTANT(T, 53, 0.50000049158540261), 55 BOOST_MATH_BIG_CONSTANT(T, 53, 1.6077979838469348), 56 BOOST_MATH_BIG_CONSTANT(T, 53, 2.5645435828098254), 57 BOOST_MATH_BIG_CONSTANT(T, 53, 2.0534873203680393), 58 BOOST_MATH_BIG_CONSTANT(T, 53, 0.74566981111565923), 59 }; 60 static const T Q_2_4[] = { 61 BOOST_MATH_BIG_CONSTANT(T, 53, 1.0), 62 BOOST_MATH_BIG_CONSTANT(T, 53, 2.8822787662376169), 63 BOOST_MATH_BIG_CONSTANT(T, 53, 4.1681660554090917), 64 BOOST_MATH_BIG_CONSTANT(T, 53, 2.7853527819234466), 65 BOOST_MATH_BIG_CONSTANT(T, 53, 0.74967671848044792), 66 BOOST_MATH_BIG_CONSTANT(T, 53, -0.00057069112416246805), 67 }; 68 // Maximum Deviation Found: 6.896e-018 69 // Expected Error Term : -6.895e-018 70 // Maximum Relative Change in Control Points : 8.497e-004 71 static const T P_4_inf[] = { 72 0.68947581948701249e-17L, 73 0.49999999999998975L, 74 1.0177274392923795L, 75 2.498208511343429L, 76 2.1921221359427595L, 77 1.5897035272532764L, 78 0.40154388356961734L, 79 }; 80 static const T Q_4_inf[] = { 81 1.0L, 82 1.7021215452463932L, 83 4.4290431747556469L, 84 2.9745631894384922L, 85 2.3013614809773616L, 86 0.28360399799075752L, 87 0.022892987908906897L, 88 }; 89 90 if(x <= 2) 91 { 92 return (offset + boost::math::tools::evaluate_polynomial(P_1_2, x) / tools::evaluate_polynomial(Q_1_2, x)) / (x * x); 93 } 94 else if(x <= 4) 95 { 96 T y = 1 / x; 97 return (1 + tools::evaluate_polynomial(P_2_4, y) / tools::evaluate_polynomial(Q_2_4, y)) / x; 98 } 99 T y = 1 / x; 100 return (1 + tools::evaluate_polynomial(P_4_inf, y) / tools::evaluate_polynomial(Q_4_inf, y)) / x; 101 } 102 103 template <class T, class Policy> 104 T trigamma_prec(T x, const mpl::int_<64>*, const Policy&) 105 { 106 // Max error in interpolated form: 1.178e-020 107 static const T offset_1_2 = BOOST_MATH_BIG_CONSTANT(T, 64, 2.109325408935546875); 108 static const T P_1_2[] = { 109 BOOST_MATH_BIG_CONSTANT(T, 64, -1.10932535608960258341), 110 BOOST_MATH_BIG_CONSTANT(T, 64, -4.18793841543017129052), 111 BOOST_MATH_BIG_CONSTANT(T, 64, -4.63865531898487734531), 112 BOOST_MATH_BIG_CONSTANT(T, 64, -0.919832884430500908047), 113 BOOST_MATH_BIG_CONSTANT(T, 64, 1.68074038333180423012), 114 BOOST_MATH_BIG_CONSTANT(T, 64, 1.21172611429185622377), 115 BOOST_MATH_BIG_CONSTANT(T, 64, 0.259635673503366427284), 116 }; 117 static const T Q_1_2[] = { 118 BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), 119 BOOST_MATH_BIG_CONSTANT(T, 64, 3.77521119359546982995), 120 BOOST_MATH_BIG_CONSTANT(T, 64, 5.664338024578956321), 121 BOOST_MATH_BIG_CONSTANT(T, 64, 4.25995134879278028361), 122 BOOST_MATH_BIG_CONSTANT(T, 64, 1.62956638448940402182), 123 BOOST_MATH_BIG_CONSTANT(T, 64, 0.259635512844691089868), 124 BOOST_MATH_BIG_CONSTANT(T, 64, 0.629642219810618032207e-8), 125 }; 126 // Max error in interpolated form: 3.912e-020 127 static const T P_2_8[] = { 128 BOOST_MATH_BIG_CONSTANT(T, 64, -0.387540035162952880976e-11), 129 BOOST_MATH_BIG_CONSTANT(T, 64, 0.500000000276430504), 130 BOOST_MATH_BIG_CONSTANT(T, 64, 3.21926880986360957306), 131 BOOST_MATH_BIG_CONSTANT(T, 64, 10.2550347708483445775), 132 BOOST_MATH_BIG_CONSTANT(T, 64, 18.9002075150709144043), 133 BOOST_MATH_BIG_CONSTANT(T, 64, 21.0357215832399705625), 134 BOOST_MATH_BIG_CONSTANT(T, 64, 13.4346512182925923978), 135 BOOST_MATH_BIG_CONSTANT(T, 64, 3.98656291026448279118), 136 }; 137 static const T Q_2_8[] = { 138 BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), 139 BOOST_MATH_BIG_CONSTANT(T, 64, 6.10520430478613667724), 140 BOOST_MATH_BIG_CONSTANT(T, 64, 18.475001060603645512), 141 BOOST_MATH_BIG_CONSTANT(T, 64, 31.7087534567758405638), 142 BOOST_MATH_BIG_CONSTANT(T, 64, 31.908814523890465398), 143 BOOST_MATH_BIG_CONSTANT(T, 64, 17.4175479039227084798), 144 BOOST_MATH_BIG_CONSTANT(T, 64, 3.98749106958394941276), 145 BOOST_MATH_BIG_CONSTANT(T, 64, -0.000115917322224411128566), 146 }; 147 // Maximum Deviation Found: 2.635e-020 148 // Expected Error Term : 2.635e-020 149 // Maximum Relative Change in Control Points : 1.791e-003 150 static const T P_8_inf[] = { 151 BOOST_MATH_BIG_CONSTANT(T, 64, -0.263527875092466899848e-19), 152 BOOST_MATH_BIG_CONSTANT(T, 64, 0.500000000000000058145), 153 BOOST_MATH_BIG_CONSTANT(T, 64, 0.0730121433777364138677), 154 BOOST_MATH_BIG_CONSTANT(T, 64, 1.94505878379957149534), 155 BOOST_MATH_BIG_CONSTANT(T, 64, 0.0517092358874932620529), 156 BOOST_MATH_BIG_CONSTANT(T, 64, 1.07995383547483921121), 157 }; 158 static const T Q_8_inf[] = { 159 BOOST_MATH_BIG_CONSTANT(T, 64, 1.0), 160 BOOST_MATH_BIG_CONSTANT(T, 64, -0.187309046577818095504), 161 BOOST_MATH_BIG_CONSTANT(T, 64, 3.95255391645238842975), 162 BOOST_MATH_BIG_CONSTANT(T, 64, -1.14743283327078949087), 163 BOOST_MATH_BIG_CONSTANT(T, 64, 2.52989799376344914499), 164 BOOST_MATH_BIG_CONSTANT(T, 64, -0.627414303172402506396), 165 BOOST_MATH_BIG_CONSTANT(T, 64, 0.141554248216425512536), 166 }; 167 168 if(x <= 2) 169 { 170 return (offset_1_2 + boost::math::tools::evaluate_polynomial(P_1_2, x) / tools::evaluate_polynomial(Q_1_2, x)) / (x * x); 171 } 172 else if(x <= 8) 173 { 174 T y = 1 / x; 175 return (1 + tools::evaluate_polynomial(P_2_8, y) / tools::evaluate_polynomial(Q_2_8, y)) / x; 176 } 177 T y = 1 / x; 178 return (1 + tools::evaluate_polynomial(P_8_inf, y) / tools::evaluate_polynomial(Q_8_inf, y)) / x; 179 } 180 181 template <class T, class Policy> 182 T trigamma_prec(T x, const mpl::int_<113>*, const Policy&) 183 { 184 // Max error in interpolated form: 1.916e-035 185 186 static const T P_1_2[] = { 187 BOOST_MATH_BIG_CONSTANT(T, 113, -0.999999999999999082554457936871832533), 188 BOOST_MATH_BIG_CONSTANT(T, 113, -4.71237311120865266379041700054847734), 189 BOOST_MATH_BIG_CONSTANT(T, 113, -7.94125711970499027763789342500817316), 190 BOOST_MATH_BIG_CONSTANT(T, 113, -5.74657746697664735258222071695644535), 191 BOOST_MATH_BIG_CONSTANT(T, 113, -0.404213349456398905981223965160595687), 192 BOOST_MATH_BIG_CONSTANT(T, 113, 2.47877781178642876561595890095758896), 193 BOOST_MATH_BIG_CONSTANT(T, 113, 2.07714151702455125992166949812126433), 194 BOOST_MATH_BIG_CONSTANT(T, 113, 0.858877899162360138844032265418028567), 195 BOOST_MATH_BIG_CONSTANT(T, 113, 0.20499222604410032375789018837922397), 196 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0272103140348194747360175268778415049), 197 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0015764849020876949848954081173520686), 198 }; 199 static const T Q_1_2[] = { 200 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 201 BOOST_MATH_BIG_CONSTANT(T, 113, 4.71237311120863419878375031457715223), 202 BOOST_MATH_BIG_CONSTANT(T, 113, 9.58619118655339853449127952145877467), 203 BOOST_MATH_BIG_CONSTANT(T, 113, 11.0940067269829372437561421279054968), 204 BOOST_MATH_BIG_CONSTANT(T, 113, 8.09075424749327792073276309969037885), 205 BOOST_MATH_BIG_CONSTANT(T, 113, 3.87705890159891405185343806884451286), 206 BOOST_MATH_BIG_CONSTANT(T, 113, 1.22758678701914477836330837816976782), 207 BOOST_MATH_BIG_CONSTANT(T, 113, 0.249092040606385004109672077814668716), 208 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0295750413900655597027079600025569048), 209 BOOST_MATH_BIG_CONSTANT(T, 113, 0.00157648490200498142247694709728858139), 210 BOOST_MATH_BIG_CONSTANT(T, 113, 0.161264050344059471721062360645432809e-14), 211 }; 212 213 // Max error in interpolated form: 8.958e-035 214 static const T P_2_4[] = { 215 BOOST_MATH_BIG_CONSTANT(T, 113, -2.55843734739907925764326773972215085), 216 BOOST_MATH_BIG_CONSTANT(T, 113, -12.2830208240542011967952466273455887), 217 BOOST_MATH_BIG_CONSTANT(T, 113, -23.9195022162767993526575786066414403), 218 BOOST_MATH_BIG_CONSTANT(T, 113, -24.9256431504823483094158828285470862), 219 BOOST_MATH_BIG_CONSTANT(T, 113, -14.7979122765478779075108064826412285), 220 BOOST_MATH_BIG_CONSTANT(T, 113, -4.46654453928610666393276765059122272), 221 BOOST_MATH_BIG_CONSTANT(T, 113, -0.0191439033405649675717082465687845002), 222 BOOST_MATH_BIG_CONSTANT(T, 113, 0.515412052554351265708917209749037352), 223 BOOST_MATH_BIG_CONSTANT(T, 113, 0.195378348786064304378247325360320038), 224 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0334761282624174313035014426794245393), 225 BOOST_MATH_BIG_CONSTANT(T, 113, 0.002373665205942206348500250056602687), 226 }; 227 static const T Q_2_4[] = { 228 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 229 BOOST_MATH_BIG_CONSTANT(T, 113, 4.80098558454419907830670928248659245), 230 BOOST_MATH_BIG_CONSTANT(T, 113, 9.99220727843170133895059300223445265), 231 BOOST_MATH_BIG_CONSTANT(T, 113, 11.8896146167631330735386697123464976), 232 BOOST_MATH_BIG_CONSTANT(T, 113, 8.96613256683809091593793565879092581), 233 BOOST_MATH_BIG_CONSTANT(T, 113, 4.47254136149624110878909334574485751), 234 BOOST_MATH_BIG_CONSTANT(T, 113, 1.48600982028196527372434773913633152), 235 BOOST_MATH_BIG_CONSTANT(T, 113, 0.319570735766764237068541501137990078), 236 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0407358345787680953107374215319322066), 237 BOOST_MATH_BIG_CONSTANT(T, 113, 0.00237366520593271641375755486420859837), 238 BOOST_MATH_BIG_CONSTANT(T, 113, 0.239554887903526152679337256236302116e-15), 239 BOOST_MATH_BIG_CONSTANT(T, 113, -0.294749244740618656265237072002026314e-17), 240 }; 241 242 static const T y_offset_2_4 = BOOST_MATH_BIG_CONSTANT(T, 113, 3.558437347412109375); 243 244 // Max error in interpolated form: 4.319e-035 245 static const T P_4_8[] = { 246 BOOST_MATH_BIG_CONSTANT(T, 113, 0.166626112697021464248967707021688845e-16), 247 BOOST_MATH_BIG_CONSTANT(T, 113, 0.499999999999997739552090249208808197), 248 BOOST_MATH_BIG_CONSTANT(T, 113, 6.40270945019053817915772473771553187), 249 BOOST_MATH_BIG_CONSTANT(T, 113, 41.3833374155000608013677627389343329), 250 BOOST_MATH_BIG_CONSTANT(T, 113, 166.803341854562809335667241074035245), 251 BOOST_MATH_BIG_CONSTANT(T, 113, 453.39964786925369319960722793414521), 252 BOOST_MATH_BIG_CONSTANT(T, 113, 851.153712317697055375935433362983944), 253 BOOST_MATH_BIG_CONSTANT(T, 113, 1097.70657567285059133109286478004458), 254 BOOST_MATH_BIG_CONSTANT(T, 113, 938.431232478455316020076349367632922), 255 BOOST_MATH_BIG_CONSTANT(T, 113, 487.268001604651932322080970189930074), 256 BOOST_MATH_BIG_CONSTANT(T, 113, 119.953445242335730062471193124820659), 257 }; 258 static const T Q_4_8[] = { 259 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 260 BOOST_MATH_BIG_CONSTANT(T, 113, 12.4720855670474488978638945855932398), 261 BOOST_MATH_BIG_CONSTANT(T, 113, 78.6093129753298570701376952709727391), 262 BOOST_MATH_BIG_CONSTANT(T, 113, 307.470246050318322489781182863190127), 263 BOOST_MATH_BIG_CONSTANT(T, 113, 805.140686101151538537565264188630079), 264 BOOST_MATH_BIG_CONSTANT(T, 113, 1439.12019760292146454787601409644413), 265 BOOST_MATH_BIG_CONSTANT(T, 113, 1735.6105285756048831268586001383127), 266 BOOST_MATH_BIG_CONSTANT(T, 113, 1348.32500712856328019355198611280536), 267 BOOST_MATH_BIG_CONSTANT(T, 113, 607.225985860570846699704222144650563), 268 BOOST_MATH_BIG_CONSTANT(T, 113, 119.952317857277045332558673164517227), 269 BOOST_MATH_BIG_CONSTANT(T, 113, 0.000140165918355036060868680809129436084), 270 }; 271 272 // Maximum Deviation Found: 2.867e-035 273 // Expected Error Term : 2.866e-035 274 // Maximum Relative Change in Control Points : 2.662e-004 275 static const T P_8_16[] = { 276 BOOST_MATH_BIG_CONSTANT(T, 113, -0.184828315274146610610872315609837439e-19), 277 BOOST_MATH_BIG_CONSTANT(T, 113, 0.500000000000000004122475157735807738), 278 BOOST_MATH_BIG_CONSTANT(T, 113, 3.02533865247313349284875558880415875), 279 BOOST_MATH_BIG_CONSTANT(T, 113, 13.5995927517457371243039532492642734), 280 BOOST_MATH_BIG_CONSTANT(T, 113, 35.3132224283087906757037999452941588), 281 BOOST_MATH_BIG_CONSTANT(T, 113, 67.1639424550714159157603179911505619), 282 BOOST_MATH_BIG_CONSTANT(T, 113, 83.5767733658513967581959839367419891), 283 BOOST_MATH_BIG_CONSTANT(T, 113, 71.073491212235705900866411319363501), 284 BOOST_MATH_BIG_CONSTANT(T, 113, 35.8621515614725564575893663483998663), 285 BOOST_MATH_BIG_CONSTANT(T, 113, 8.72152231639983491987779743154333318), 286 }; 287 static const T Q_8_16[] = { 288 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 289 BOOST_MATH_BIG_CONSTANT(T, 113, 5.71734397161293452310624822415866372), 290 BOOST_MATH_BIG_CONSTANT(T, 113, 25.293404179620438179337103263274815), 291 BOOST_MATH_BIG_CONSTANT(T, 113, 62.2619767967468199111077640625328469), 292 BOOST_MATH_BIG_CONSTANT(T, 113, 113.955048909238993473389714972250235), 293 BOOST_MATH_BIG_CONSTANT(T, 113, 130.807138328938966981862203944329408), 294 BOOST_MATH_BIG_CONSTANT(T, 113, 102.423146902337654110717764213057753), 295 BOOST_MATH_BIG_CONSTANT(T, 113, 44.0424772805245202514468199602123565), 296 BOOST_MATH_BIG_CONSTANT(T, 113, 8.89898032477904072082994913461386099), 297 BOOST_MATH_BIG_CONSTANT(T, 113, -0.0296627336872039988632793863671456398), 298 }; 299 // Maximum Deviation Found: 1.079e-035 300 // Expected Error Term : -1.079e-035 301 // Maximum Relative Change in Control Points : 7.884e-003 302 static const T P_16_inf[] = { 303 BOOST_MATH_BIG_CONSTANT(T, 113, 0.0), 304 BOOST_MATH_BIG_CONSTANT(T, 113, 0.500000000000000000000000000000087317), 305 BOOST_MATH_BIG_CONSTANT(T, 113, 0.345625669885456215194494735902663968), 306 BOOST_MATH_BIG_CONSTANT(T, 113, 9.62895499360842232127552650044647769), 307 BOOST_MATH_BIG_CONSTANT(T, 113, 3.5936085382439026269301003761320812), 308 BOOST_MATH_BIG_CONSTANT(T, 113, 49.459599118438883265036646019410669), 309 BOOST_MATH_BIG_CONSTANT(T, 113, 7.77519237321893917784735690560496607), 310 BOOST_MATH_BIG_CONSTANT(T, 113, 74.4536074488178075948642351179304121), 311 BOOST_MATH_BIG_CONSTANT(T, 113, 2.75209340397069050436806159297952699), 312 BOOST_MATH_BIG_CONSTANT(T, 113, 23.9292359711471667884504840186561598), 313 }; 314 static const T Q_16_inf[] = { 315 BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), 316 BOOST_MATH_BIG_CONSTANT(T, 113, 0.357918006437579097055656138920742037), 317 BOOST_MATH_BIG_CONSTANT(T, 113, 19.1386039850709849435325005484512944), 318 BOOST_MATH_BIG_CONSTANT(T, 113, 0.874349081464143606016221431763364517), 319 BOOST_MATH_BIG_CONSTANT(T, 113, 98.6516097434855572678195488061432509), 320 BOOST_MATH_BIG_CONSTANT(T, 113, -16.1051972833382893468655223662534306), 321 BOOST_MATH_BIG_CONSTANT(T, 113, 154.316860216253720989145047141653727), 322 BOOST_MATH_BIG_CONSTANT(T, 113, -40.2026880424378986053105969312264534), 323 BOOST_MATH_BIG_CONSTANT(T, 113, 60.1679136674264778074736441126810223), 324 BOOST_MATH_BIG_CONSTANT(T, 113, -13.3414844622256422644504472438320114), 325 BOOST_MATH_BIG_CONSTANT(T, 113, 2.53795636200649908779512969030363442), 326 }; 327 328 if(x <= 2) 329 { 330 return (2 + boost::math::tools::evaluate_polynomial(P_1_2, x) / tools::evaluate_polynomial(Q_1_2, x)) / (x * x); 331 } 332 else if(x <= 4) 333 { 334 return (y_offset_2_4 + boost::math::tools::evaluate_polynomial(P_2_4, x) / tools::evaluate_polynomial(Q_2_4, x)) / (x * x); 335 } 336 else if(x <= 8) 337 { 338 T y = 1 / x; 339 return (1 + tools::evaluate_polynomial(P_4_8, y) / tools::evaluate_polynomial(Q_4_8, y)) / x; 340 } 341 else if(x <= 16) 342 { 343 T y = 1 / x; 344 return (1 + tools::evaluate_polynomial(P_8_16, y) / tools::evaluate_polynomial(Q_8_16, y)) / x; 345 } 346 T y = 1 / x; 347 return (1 + tools::evaluate_polynomial(P_16_inf, y) / tools::evaluate_polynomial(Q_16_inf, y)) / x; 348 } 349 350 template <class T, class Tag, class Policy> 351 T trigamma_imp(T x, const Tag* t, const Policy& pol) 352 { 353 // 354 // This handles reflection of negative arguments, and all our 355 // error handling, then forwards to the T-specific approximation. 356 // 357 BOOST_MATH_STD_USING // ADL of std functions. 358 359 T result = 0; 360 // 361 // Check for negative arguments and use reflection: 362 // 363 if(x <= 0) 364 { 365 // Reflect: 366 T z = 1 - x; 367 // Argument reduction for tan: 368 if(floor(x) == x) 369 { 370 return policies::raise_pole_error<T>("boost::math::trigamma<%1%>(%1%)", 0, (1-x), pol); 371 } 372 T s = fabs(x) < fabs(z) ? boost::math::sin_pi(x, pol) : boost::math::sin_pi(z, pol); 373 return -trigamma_imp(z, t, pol) + boost::math::pow<2>(constants::pi<T>()) / (s * s); 374 } 375 if(x < 1) 376 { 377 result = 1 / (x * x); 378 x += 1; 379 } 380 return result + trigamma_prec(x, t, pol); 381 } 382 383 template <class T, class Policy> 384 T trigamma_imp(T x, const mpl::int_<0>*, const Policy& pol) 385 { 386 return polygamma_imp(1, x, pol); 387 } 388 // 389 // Initializer: ensure all our constants are initialized prior to the first call of main: 390 // 391 template <class T, class Policy> 392 struct trigamma_initializer 393 { 394 struct init 395 { initboost::math::detail::trigamma_initializer::init396 init() 397 { 398 typedef typename policies::precision<T, Policy>::type precision_type; 399 do_init(mpl::bool_<precision_type::value && (precision_type::value <= 113)>()); 400 } do_initboost::math::detail::trigamma_initializer::init401 void do_init(const mpl::true_&) 402 { 403 boost::math::trigamma(T(2.5), Policy()); 404 } do_initboost::math::detail::trigamma_initializer::init405 void do_init(const mpl::false_&){} force_instantiateboost::math::detail::trigamma_initializer::init406 void force_instantiate()const{} 407 }; 408 static const init initializer; force_instantiateboost::math::detail::trigamma_initializer409 static void force_instantiate() 410 { 411 initializer.force_instantiate(); 412 } 413 }; 414 415 template <class T, class Policy> 416 const typename trigamma_initializer<T, Policy>::init trigamma_initializer<T, Policy>::initializer; 417 418 } // namespace detail 419 420 template <class T, class Policy> 421 inline typename tools::promote_args<T>::type trigamma(T x,const Policy &)422 trigamma(T x, const Policy&) 423 { 424 typedef typename tools::promote_args<T>::type result_type; 425 typedef typename policies::evaluation<result_type, Policy>::type value_type; 426 typedef typename policies::precision<T, Policy>::type precision_type; 427 typedef typename mpl::if_< 428 mpl::or_< 429 mpl::less_equal<precision_type, mpl::int_<0> >, 430 mpl::greater<precision_type, mpl::int_<114> > 431 >, 432 mpl::int_<0>, 433 typename mpl::if_< 434 mpl::less<precision_type, mpl::int_<54> >, 435 mpl::int_<53>, 436 typename mpl::if_< 437 mpl::less<precision_type, mpl::int_<65> >, 438 mpl::int_<64>, 439 mpl::int_<113> 440 >::type 441 >::type 442 >::type tag_type; 443 444 typedef typename policies::normalise< 445 Policy, 446 policies::promote_float<false>, 447 policies::promote_double<false>, 448 policies::discrete_quantile<>, 449 policies::assert_undefined<> >::type forwarding_policy; 450 451 // Force initialization of constants: 452 detail::trigamma_initializer<value_type, forwarding_policy>::force_instantiate(); 453 454 return policies::checked_narrowing_cast<result_type, Policy>(detail::trigamma_imp( 455 static_cast<value_type>(x), 456 static_cast<const tag_type*>(0), forwarding_policy()), "boost::math::trigamma<%1%>(%1%)"); 457 } 458 459 template <class T> 460 inline typename tools::promote_args<T>::type trigamma(T x)461 trigamma(T x) 462 { 463 return trigamma(x, policies::policy<>()); 464 } 465 466 } // namespace math 467 } // namespace boost 468 #endif 469 470