diff options
Diffstat (limited to 'src/third_party/boost-1.69.0/boost/math/special_functions/detail/unchecked_factorial.hpp')
-rw-r--r-- | src/third_party/boost-1.69.0/boost/math/special_functions/detail/unchecked_factorial.hpp | 805 |
1 files changed, 805 insertions, 0 deletions
diff --git a/src/third_party/boost-1.69.0/boost/math/special_functions/detail/unchecked_factorial.hpp b/src/third_party/boost-1.69.0/boost/math/special_functions/detail/unchecked_factorial.hpp new file mode 100644 index 00000000000..17366742c46 --- /dev/null +++ b/src/third_party/boost-1.69.0/boost/math/special_functions/detail/unchecked_factorial.hpp @@ -0,0 +1,805 @@ +// 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_SP_UC_FACTORIALS_HPP +#define BOOST_MATH_SP_UC_FACTORIALS_HPP + +#ifdef _MSC_VER +#pragma once +#endif + +#ifdef BOOST_MSVC +#pragma warning(push) // Temporary until lexical cast fixed. +#pragma warning(disable: 4127 4701) +#endif +#ifndef BOOST_MATH_NO_LEXICAL_CAST +#include <boost/lexical_cast.hpp> +#endif +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif +#include <cmath> +#include <boost/math/special_functions/math_fwd.hpp> + +#ifdef BOOST_MATH_HAVE_CONSTEXPR_TABLES +#include <array> +#else +#include <boost/array.hpp> +#endif + +namespace boost { namespace math +{ +// Forward declarations: +template <class T> +struct max_factorial; + +// Definitions: +template <> +inline BOOST_MATH_CONSTEXPR_TABLE_FUNCTION float unchecked_factorial<float>(unsigned i BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(float)) +{ +#ifdef BOOST_MATH_HAVE_CONSTEXPR_TABLES + constexpr std::array<float, 35> factorials = { { +#else + static const boost::array<float, 35> factorials = {{ +#endif + 1.0F, + 1.0F, + 2.0F, + 6.0F, + 24.0F, + 120.0F, + 720.0F, + 5040.0F, + 40320.0F, + 362880.0F, + 3628800.0F, + 39916800.0F, + 479001600.0F, + 6227020800.0F, + 87178291200.0F, + 1307674368000.0F, + 20922789888000.0F, + 355687428096000.0F, + 6402373705728000.0F, + 121645100408832000.0F, + 0.243290200817664e19F, + 0.5109094217170944e20F, + 0.112400072777760768e22F, + 0.2585201673888497664e23F, + 0.62044840173323943936e24F, + 0.15511210043330985984e26F, + 0.403291461126605635584e27F, + 0.10888869450418352160768e29F, + 0.304888344611713860501504e30F, + 0.8841761993739701954543616e31F, + 0.26525285981219105863630848e33F, + 0.822283865417792281772556288e34F, + 0.26313083693369353016721801216e36F, + 0.868331761881188649551819440128e37F, + 0.29523279903960414084761860964352e39F, + }}; + + return factorials[i]; +} + +template <> +struct max_factorial<float> +{ + BOOST_STATIC_CONSTANT(unsigned, value = 34); +}; + + +template <> +inline BOOST_MATH_CONSTEXPR_TABLE_FUNCTION long double unchecked_factorial<long double>(unsigned i BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(long double)) +{ +#ifdef BOOST_MATH_HAVE_CONSTEXPR_TABLES + constexpr std::array<long double, 171> factorials = { { +#else + static const boost::array<long double, 171> factorials = {{ +#endif + 1L, + 1L, + 2L, + 6L, + 24L, + 120L, + 720L, + 5040L, + 40320L, + 362880.0L, + 3628800.0L, + 39916800.0L, + 479001600.0L, + 6227020800.0L, + 87178291200.0L, + 1307674368000.0L, + 20922789888000.0L, + 355687428096000.0L, + 6402373705728000.0L, + 121645100408832000.0L, + 0.243290200817664e19L, + 0.5109094217170944e20L, + 0.112400072777760768e22L, + 0.2585201673888497664e23L, + 0.62044840173323943936e24L, + 0.15511210043330985984e26L, + 0.403291461126605635584e27L, + 0.10888869450418352160768e29L, + 0.304888344611713860501504e30L, + 0.8841761993739701954543616e31L, + 0.26525285981219105863630848e33L, + 0.822283865417792281772556288e34L, + 0.26313083693369353016721801216e36L, + 0.868331761881188649551819440128e37L, + 0.29523279903960414084761860964352e39L, + 0.103331479663861449296666513375232e41L, + 0.3719933267899012174679994481508352e42L, + 0.137637530912263450463159795815809024e44L, + 0.5230226174666011117600072241000742912e45L, + 0.203978820811974433586402817399028973568e47L, + 0.815915283247897734345611269596115894272e48L, + 0.3345252661316380710817006205344075166515e50L, + 0.1405006117752879898543142606244511569936e52L, + 0.6041526306337383563735513206851399750726e53L, + 0.265827157478844876804362581101461589032e55L, + 0.1196222208654801945619631614956577150644e57L, + 0.5502622159812088949850305428800254892962e58L, + 0.2586232415111681806429643551536119799692e60L, + 0.1241391559253607267086228904737337503852e62L, + 0.6082818640342675608722521633212953768876e63L, + 0.3041409320171337804361260816606476884438e65L, + 0.1551118753287382280224243016469303211063e67L, + 0.8065817517094387857166063685640376697529e68L, + 0.427488328406002556429801375338939964969e70L, + 0.2308436973392413804720927426830275810833e72L, + 0.1269640335365827592596510084756651695958e74L, + 0.7109985878048634518540456474637249497365e75L, + 0.4052691950487721675568060190543232213498e77L, + 0.2350561331282878571829474910515074683829e79L, + 0.1386831185456898357379390197203894063459e81L, + 0.8320987112741390144276341183223364380754e82L, + 0.507580213877224798800856812176625227226e84L, + 0.3146997326038793752565312235495076408801e86L, + 0.1982608315404440064116146708361898137545e88L, + 0.1268869321858841641034333893351614808029e90L, + 0.8247650592082470666723170306785496252186e91L, + 0.5443449390774430640037292402478427526443e93L, + 0.3647111091818868528824985909660546442717e95L, + 0.2480035542436830599600990418569171581047e97L, + 0.1711224524281413113724683388812728390923e99L, + 0.1197857166996989179607278372168909873646e101L, + 0.8504785885678623175211676442399260102886e102L, + 0.6123445837688608686152407038527467274078e104L, + 0.4470115461512684340891257138125051110077e106L, + 0.3307885441519386412259530282212537821457e108L, + 0.2480914081139539809194647711659403366093e110L, + 0.188549470166605025498793226086114655823e112L, + 0.1451830920282858696340707840863082849837e114L, + 0.1132428117820629783145752115873204622873e116L, + 0.8946182130782975286851441715398316520698e117L, + 0.7156945704626380229481153372318653216558e119L, + 0.5797126020747367985879734231578109105412e121L, + 0.4753643337012841748421382069894049466438e123L, + 0.3945523969720658651189747118012061057144e125L, + 0.3314240134565353266999387579130131288001e127L, + 0.2817104114380550276949479442260611594801e129L, + 0.2422709538367273238176552320344125971528e131L, + 0.210775729837952771721360051869938959523e133L, + 0.1854826422573984391147968456455462843802e135L, + 0.1650795516090846108121691926245361930984e137L, + 0.1485715964481761497309522733620825737886e139L, + 0.1352001527678402962551665687594951421476e141L, + 0.1243841405464130725547532432587355307758e143L, + 0.1156772507081641574759205162306240436215e145L, + 0.1087366156656743080273652852567866010042e147L, + 0.103299784882390592625997020993947270954e149L, + 0.9916779348709496892095714015418938011582e150L, + 0.9619275968248211985332842594956369871234e152L, + 0.942689044888324774562618574305724247381e154L, + 0.9332621544394415268169923885626670049072e156L, + 0.9332621544394415268169923885626670049072e158L, + 0.9425947759838359420851623124482936749562e160L, + 0.9614466715035126609268655586972595484554e162L, + 0.990290071648618040754671525458177334909e164L, + 0.1029901674514562762384858386476504428305e167L, + 0.1081396758240290900504101305800329649721e169L, + 0.1146280563734708354534347384148349428704e171L, + 0.1226520203196137939351751701038733888713e173L, + 0.132464181945182897449989183712183259981e175L, + 0.1443859583202493582204882102462797533793e177L, + 0.1588245541522742940425370312709077287172e179L, + 0.1762952551090244663872161047107075788761e181L, + 0.1974506857221074023536820372759924883413e183L, + 0.2231192748659813646596607021218715118256e185L, + 0.2543559733472187557120132004189335234812e187L, + 0.2925093693493015690688151804817735520034e189L, + 0.339310868445189820119825609358857320324e191L, + 0.396993716080872089540195962949863064779e193L, + 0.4684525849754290656574312362808384164393e195L, + 0.5574585761207605881323431711741977155627e197L, + 0.6689502913449127057588118054090372586753e199L, + 0.8094298525273443739681622845449350829971e201L, + 0.9875044200833601362411579871448208012564e203L, + 0.1214630436702532967576624324188129585545e206L, + 0.1506141741511140879795014161993280686076e208L, + 0.1882677176888926099743767702491600857595e210L, + 0.237217324288004688567714730513941708057e212L, + 0.3012660018457659544809977077527059692324e214L, + 0.3856204823625804217356770659234636406175e216L, + 0.4974504222477287440390234150412680963966e218L, + 0.6466855489220473672507304395536485253155e220L, + 0.8471580690878820510984568758152795681634e222L, + 0.1118248651196004307449963076076169029976e225L, + 0.1487270706090685728908450891181304809868e227L, + 0.1992942746161518876737324194182948445223e229L, + 0.269047270731805048359538766214698040105e231L, + 0.3659042881952548657689727220519893345429e233L, + 0.5012888748274991661034926292112253883237e235L, + 0.6917786472619488492228198283114910358867e237L, + 0.9615723196941089004197195613529725398826e239L, + 0.1346201247571752460587607385894161555836e242L, + 0.1898143759076170969428526414110767793728e244L, + 0.2695364137888162776588507508037290267094e246L, + 0.3854370717180072770521565736493325081944e248L, + 0.5550293832739304789551054660550388118e250L, + 0.80479260574719919448490292577980627711e252L, + 0.1174997204390910823947958271638517164581e255L, + 0.1727245890454638911203498659308620231933e257L, + 0.2556323917872865588581178015776757943262e259L, + 0.380892263763056972698595524350736933546e261L, + 0.571338395644585459047893286526105400319e263L, + 0.8627209774233240431623188626544191544816e265L, + 0.1311335885683452545606724671234717114812e268L, + 0.2006343905095682394778288746989117185662e270L, + 0.308976961384735088795856467036324046592e272L, + 0.4789142901463393876335775239063022722176e274L, + 0.7471062926282894447083809372938315446595e276L, + 0.1172956879426414428192158071551315525115e279L, + 0.1853271869493734796543609753051078529682e281L, + 0.2946702272495038326504339507351214862195e283L, + 0.4714723635992061322406943211761943779512e285L, + 0.7590705053947218729075178570936729485014e287L, + 0.1229694218739449434110178928491750176572e290L, + 0.2004401576545302577599591653441552787813e292L, + 0.3287218585534296227263330311644146572013e294L, + 0.5423910666131588774984495014212841843822e296L, + 0.9003691705778437366474261723593317460744e298L, + 0.1503616514864999040201201707840084015944e301L, + 0.2526075744973198387538018869171341146786e303L, + 0.4269068009004705274939251888899566538069e305L, + 0.7257415615307998967396728211129263114717e307L, + }}; + + return factorials[i]; +} + +template <> +struct max_factorial<long double> +{ + BOOST_STATIC_CONSTANT(unsigned, value = 170); +}; + +#ifdef BOOST_MATH_USE_FLOAT128 + +template <> +inline BOOST_MATH_CONSTEXPR_TABLE_FUNCTION BOOST_MATH_FLOAT128_TYPE unchecked_factorial<BOOST_MATH_FLOAT128_TYPE>(unsigned i) +{ +#ifdef BOOST_MATH_HAVE_CONSTEXPR_TABLES + constexpr std::array<BOOST_MATH_FLOAT128_TYPE, 171> factorials = { { +#else + static const boost::array<BOOST_MATH_FLOAT128_TYPE, 171> factorials = { { +#endif + 1, + 1, + 2, + 6, + 24, + 120, + 720, + 5040, + 40320, + 362880.0Q, + 3628800.0Q, + 39916800.0Q, + 479001600.0Q, + 6227020800.0Q, + 87178291200.0Q, + 1307674368000.0Q, + 20922789888000.0Q, + 355687428096000.0Q, + 6402373705728000.0Q, + 121645100408832000.0Q, + 0.243290200817664e19Q, + 0.5109094217170944e20Q, + 0.112400072777760768e22Q, + 0.2585201673888497664e23Q, + 0.62044840173323943936e24Q, + 0.15511210043330985984e26Q, + 0.403291461126605635584e27Q, + 0.10888869450418352160768e29Q, + 0.304888344611713860501504e30Q, + 0.8841761993739701954543616e31Q, + 0.26525285981219105863630848e33Q, + 0.822283865417792281772556288e34Q, + 0.26313083693369353016721801216e36Q, + 0.868331761881188649551819440128e37Q, + 0.29523279903960414084761860964352e39Q, + 0.103331479663861449296666513375232e41Q, + 0.3719933267899012174679994481508352e42Q, + 0.137637530912263450463159795815809024e44Q, + 0.5230226174666011117600072241000742912e45Q, + 0.203978820811974433586402817399028973568e47Q, + 0.815915283247897734345611269596115894272e48Q, + 0.3345252661316380710817006205344075166515e50Q, + 0.1405006117752879898543142606244511569936e52Q, + 0.6041526306337383563735513206851399750726e53Q, + 0.265827157478844876804362581101461589032e55Q, + 0.1196222208654801945619631614956577150644e57Q, + 0.5502622159812088949850305428800254892962e58Q, + 0.2586232415111681806429643551536119799692e60Q, + 0.1241391559253607267086228904737337503852e62Q, + 0.6082818640342675608722521633212953768876e63Q, + 0.3041409320171337804361260816606476884438e65Q, + 0.1551118753287382280224243016469303211063e67Q, + 0.8065817517094387857166063685640376697529e68Q, + 0.427488328406002556429801375338939964969e70Q, + 0.2308436973392413804720927426830275810833e72Q, + 0.1269640335365827592596510084756651695958e74Q, + 0.7109985878048634518540456474637249497365e75Q, + 0.4052691950487721675568060190543232213498e77Q, + 0.2350561331282878571829474910515074683829e79Q, + 0.1386831185456898357379390197203894063459e81Q, + 0.8320987112741390144276341183223364380754e82Q, + 0.507580213877224798800856812176625227226e84Q, + 0.3146997326038793752565312235495076408801e86Q, + 0.1982608315404440064116146708361898137545e88Q, + 0.1268869321858841641034333893351614808029e90Q, + 0.8247650592082470666723170306785496252186e91Q, + 0.5443449390774430640037292402478427526443e93Q, + 0.3647111091818868528824985909660546442717e95Q, + 0.2480035542436830599600990418569171581047e97Q, + 0.1711224524281413113724683388812728390923e99Q, + 0.1197857166996989179607278372168909873646e101Q, + 0.8504785885678623175211676442399260102886e102Q, + 0.6123445837688608686152407038527467274078e104Q, + 0.4470115461512684340891257138125051110077e106Q, + 0.3307885441519386412259530282212537821457e108Q, + 0.2480914081139539809194647711659403366093e110Q, + 0.188549470166605025498793226086114655823e112Q, + 0.1451830920282858696340707840863082849837e114Q, + 0.1132428117820629783145752115873204622873e116Q, + 0.8946182130782975286851441715398316520698e117Q, + 0.7156945704626380229481153372318653216558e119Q, + 0.5797126020747367985879734231578109105412e121Q, + 0.4753643337012841748421382069894049466438e123Q, + 0.3945523969720658651189747118012061057144e125Q, + 0.3314240134565353266999387579130131288001e127Q, + 0.2817104114380550276949479442260611594801e129Q, + 0.2422709538367273238176552320344125971528e131Q, + 0.210775729837952771721360051869938959523e133Q, + 0.1854826422573984391147968456455462843802e135Q, + 0.1650795516090846108121691926245361930984e137Q, + 0.1485715964481761497309522733620825737886e139Q, + 0.1352001527678402962551665687594951421476e141Q, + 0.1243841405464130725547532432587355307758e143Q, + 0.1156772507081641574759205162306240436215e145Q, + 0.1087366156656743080273652852567866010042e147Q, + 0.103299784882390592625997020993947270954e149Q, + 0.9916779348709496892095714015418938011582e150Q, + 0.9619275968248211985332842594956369871234e152Q, + 0.942689044888324774562618574305724247381e154Q, + 0.9332621544394415268169923885626670049072e156Q, + 0.9332621544394415268169923885626670049072e158Q, + 0.9425947759838359420851623124482936749562e160Q, + 0.9614466715035126609268655586972595484554e162Q, + 0.990290071648618040754671525458177334909e164Q, + 0.1029901674514562762384858386476504428305e167Q, + 0.1081396758240290900504101305800329649721e169Q, + 0.1146280563734708354534347384148349428704e171Q, + 0.1226520203196137939351751701038733888713e173Q, + 0.132464181945182897449989183712183259981e175Q, + 0.1443859583202493582204882102462797533793e177Q, + 0.1588245541522742940425370312709077287172e179Q, + 0.1762952551090244663872161047107075788761e181Q, + 0.1974506857221074023536820372759924883413e183Q, + 0.2231192748659813646596607021218715118256e185Q, + 0.2543559733472187557120132004189335234812e187Q, + 0.2925093693493015690688151804817735520034e189Q, + 0.339310868445189820119825609358857320324e191Q, + 0.396993716080872089540195962949863064779e193Q, + 0.4684525849754290656574312362808384164393e195Q, + 0.5574585761207605881323431711741977155627e197Q, + 0.6689502913449127057588118054090372586753e199Q, + 0.8094298525273443739681622845449350829971e201Q, + 0.9875044200833601362411579871448208012564e203Q, + 0.1214630436702532967576624324188129585545e206Q, + 0.1506141741511140879795014161993280686076e208Q, + 0.1882677176888926099743767702491600857595e210Q, + 0.237217324288004688567714730513941708057e212Q, + 0.3012660018457659544809977077527059692324e214Q, + 0.3856204823625804217356770659234636406175e216Q, + 0.4974504222477287440390234150412680963966e218Q, + 0.6466855489220473672507304395536485253155e220Q, + 0.8471580690878820510984568758152795681634e222Q, + 0.1118248651196004307449963076076169029976e225Q, + 0.1487270706090685728908450891181304809868e227Q, + 0.1992942746161518876737324194182948445223e229Q, + 0.269047270731805048359538766214698040105e231Q, + 0.3659042881952548657689727220519893345429e233Q, + 0.5012888748274991661034926292112253883237e235Q, + 0.6917786472619488492228198283114910358867e237Q, + 0.9615723196941089004197195613529725398826e239Q, + 0.1346201247571752460587607385894161555836e242Q, + 0.1898143759076170969428526414110767793728e244Q, + 0.2695364137888162776588507508037290267094e246Q, + 0.3854370717180072770521565736493325081944e248Q, + 0.5550293832739304789551054660550388118e250Q, + 0.80479260574719919448490292577980627711e252Q, + 0.1174997204390910823947958271638517164581e255Q, + 0.1727245890454638911203498659308620231933e257Q, + 0.2556323917872865588581178015776757943262e259Q, + 0.380892263763056972698595524350736933546e261Q, + 0.571338395644585459047893286526105400319e263Q, + 0.8627209774233240431623188626544191544816e265Q, + 0.1311335885683452545606724671234717114812e268Q, + 0.2006343905095682394778288746989117185662e270Q, + 0.308976961384735088795856467036324046592e272Q, + 0.4789142901463393876335775239063022722176e274Q, + 0.7471062926282894447083809372938315446595e276Q, + 0.1172956879426414428192158071551315525115e279Q, + 0.1853271869493734796543609753051078529682e281Q, + 0.2946702272495038326504339507351214862195e283Q, + 0.4714723635992061322406943211761943779512e285Q, + 0.7590705053947218729075178570936729485014e287Q, + 0.1229694218739449434110178928491750176572e290Q, + 0.2004401576545302577599591653441552787813e292Q, + 0.3287218585534296227263330311644146572013e294Q, + 0.5423910666131588774984495014212841843822e296Q, + 0.9003691705778437366474261723593317460744e298Q, + 0.1503616514864999040201201707840084015944e301Q, + 0.2526075744973198387538018869171341146786e303Q, + 0.4269068009004705274939251888899566538069e305Q, + 0.7257415615307998967396728211129263114717e307Q, + } }; + + return factorials[i]; +} + +template <> +struct max_factorial<BOOST_MATH_FLOAT128_TYPE> +{ + BOOST_STATIC_CONSTANT(unsigned, value = 170); +}; + +#endif + +template <> +inline BOOST_MATH_CONSTEXPR_TABLE_FUNCTION double unchecked_factorial<double>(unsigned i BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(double)) +{ + return static_cast<double>(boost::math::unchecked_factorial<long double>(i)); +} + +template <> +struct max_factorial<double> +{ + BOOST_STATIC_CONSTANT(unsigned, + value = ::boost::math::max_factorial<long double>::value); +}; + +#ifndef BOOST_MATH_NO_LEXICAL_CAST + +template <class T> +struct unchecked_factorial_initializer +{ + struct init + { + init() + { + boost::math::unchecked_factorial<T>(3); + } + void force_instantiate()const {} + }; + static const init initializer; + static void force_instantiate() + { + initializer.force_instantiate(); + } +}; + +template <class T> +const typename unchecked_factorial_initializer<T>::init unchecked_factorial_initializer<T>::initializer; + + +template <class T, int N> +inline T unchecked_factorial_imp(unsigned i, const mpl::int_<N>&) +{ + BOOST_STATIC_ASSERT(!boost::is_integral<T>::value); + // factorial<unsigned int>(n) is not implemented + // because it would overflow integral type T for too small n + // to be useful. Use instead a floating-point type, + // and convert to an unsigned type if essential, for example: + // unsigned int nfac = static_cast<unsigned int>(factorial<double>(n)); + // See factorial documentation for more detail. + + unchecked_factorial_initializer<T>::force_instantiate(); + + static const boost::array<T, 101> factorials = {{ + T(boost::math::tools::convert_from_string<T>("1")), + T(boost::math::tools::convert_from_string<T>("1")), + T(boost::math::tools::convert_from_string<T>("2")), + T(boost::math::tools::convert_from_string<T>("6")), + T(boost::math::tools::convert_from_string<T>("24")), + T(boost::math::tools::convert_from_string<T>("120")), + T(boost::math::tools::convert_from_string<T>("720")), + T(boost::math::tools::convert_from_string<T>("5040")), + T(boost::math::tools::convert_from_string<T>("40320")), + T(boost::math::tools::convert_from_string<T>("362880")), + T(boost::math::tools::convert_from_string<T>("3628800")), + T(boost::math::tools::convert_from_string<T>("39916800")), + T(boost::math::tools::convert_from_string<T>("479001600")), + T(boost::math::tools::convert_from_string<T>("6227020800")), + T(boost::math::tools::convert_from_string<T>("87178291200")), + T(boost::math::tools::convert_from_string<T>("1307674368000")), + T(boost::math::tools::convert_from_string<T>("20922789888000")), + T(boost::math::tools::convert_from_string<T>("355687428096000")), + T(boost::math::tools::convert_from_string<T>("6402373705728000")), + T(boost::math::tools::convert_from_string<T>("121645100408832000")), + T(boost::math::tools::convert_from_string<T>("2432902008176640000")), + T(boost::math::tools::convert_from_string<T>("51090942171709440000")), + T(boost::math::tools::convert_from_string<T>("1124000727777607680000")), + T(boost::math::tools::convert_from_string<T>("25852016738884976640000")), + T(boost::math::tools::convert_from_string<T>("620448401733239439360000")), + T(boost::math::tools::convert_from_string<T>("15511210043330985984000000")), + T(boost::math::tools::convert_from_string<T>("403291461126605635584000000")), + T(boost::math::tools::convert_from_string<T>("10888869450418352160768000000")), + T(boost::math::tools::convert_from_string<T>("304888344611713860501504000000")), + T(boost::math::tools::convert_from_string<T>("8841761993739701954543616000000")), + T(boost::math::tools::convert_from_string<T>("265252859812191058636308480000000")), + T(boost::math::tools::convert_from_string<T>("8222838654177922817725562880000000")), + T(boost::math::tools::convert_from_string<T>("263130836933693530167218012160000000")), + T(boost::math::tools::convert_from_string<T>("8683317618811886495518194401280000000")), + T(boost::math::tools::convert_from_string<T>("295232799039604140847618609643520000000")), + T(boost::math::tools::convert_from_string<T>("10333147966386144929666651337523200000000")), + T(boost::math::tools::convert_from_string<T>("371993326789901217467999448150835200000000")), + T(boost::math::tools::convert_from_string<T>("13763753091226345046315979581580902400000000")), + T(boost::math::tools::convert_from_string<T>("523022617466601111760007224100074291200000000")), + T(boost::math::tools::convert_from_string<T>("20397882081197443358640281739902897356800000000")), + T(boost::math::tools::convert_from_string<T>("815915283247897734345611269596115894272000000000")), + T(boost::math::tools::convert_from_string<T>("33452526613163807108170062053440751665152000000000")), + T(boost::math::tools::convert_from_string<T>("1405006117752879898543142606244511569936384000000000")), + T(boost::math::tools::convert_from_string<T>("60415263063373835637355132068513997507264512000000000")), + T(boost::math::tools::convert_from_string<T>("2658271574788448768043625811014615890319638528000000000")), + T(boost::math::tools::convert_from_string<T>("119622220865480194561963161495657715064383733760000000000")), + T(boost::math::tools::convert_from_string<T>("5502622159812088949850305428800254892961651752960000000000")), + T(boost::math::tools::convert_from_string<T>("258623241511168180642964355153611979969197632389120000000000")), + T(boost::math::tools::convert_from_string<T>("12413915592536072670862289047373375038521486354677760000000000")), + T(boost::math::tools::convert_from_string<T>("608281864034267560872252163321295376887552831379210240000000000")), + T(boost::math::tools::convert_from_string<T>("30414093201713378043612608166064768844377641568960512000000000000")), + T(boost::math::tools::convert_from_string<T>("1551118753287382280224243016469303211063259720016986112000000000000")), + T(boost::math::tools::convert_from_string<T>("80658175170943878571660636856403766975289505440883277824000000000000")), + T(boost::math::tools::convert_from_string<T>("4274883284060025564298013753389399649690343788366813724672000000000000")), + T(boost::math::tools::convert_from_string<T>("230843697339241380472092742683027581083278564571807941132288000000000000")), + T(boost::math::tools::convert_from_string<T>("12696403353658275925965100847566516959580321051449436762275840000000000000")), + T(boost::math::tools::convert_from_string<T>("710998587804863451854045647463724949736497978881168458687447040000000000000")), + T(boost::math::tools::convert_from_string<T>("40526919504877216755680601905432322134980384796226602145184481280000000000000")), + T(boost::math::tools::convert_from_string<T>("2350561331282878571829474910515074683828862318181142924420699914240000000000000")), + T(boost::math::tools::convert_from_string<T>("138683118545689835737939019720389406345902876772687432540821294940160000000000000")), + T(boost::math::tools::convert_from_string<T>("8320987112741390144276341183223364380754172606361245952449277696409600000000000000")), + T(boost::math::tools::convert_from_string<T>("507580213877224798800856812176625227226004528988036003099405939480985600000000000000")), + T(boost::math::tools::convert_from_string<T>("31469973260387937525653122354950764088012280797258232192163168247821107200000000000000")), + T(boost::math::tools::convert_from_string<T>("1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000")), + T(boost::math::tools::convert_from_string<T>("126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000")), + T(boost::math::tools::convert_from_string<T>("8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000")), + T(boost::math::tools::convert_from_string<T>("544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000")), + T(boost::math::tools::convert_from_string<T>("36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000")), + T(boost::math::tools::convert_from_string<T>("2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000")), + T(boost::math::tools::convert_from_string<T>("171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000")), + T(boost::math::tools::convert_from_string<T>("11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000")), + T(boost::math::tools::convert_from_string<T>("850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000")), + T(boost::math::tools::convert_from_string<T>("61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000")), + T(boost::math::tools::convert_from_string<T>("4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000")), + T(boost::math::tools::convert_from_string<T>("330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000")), + T(boost::math::tools::convert_from_string<T>("24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000")), + T(boost::math::tools::convert_from_string<T>("1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000")), + T(boost::math::tools::convert_from_string<T>("145183092028285869634070784086308284983740379224208358846781574688061991349156420080065207861248000000000000000000")), + T(boost::math::tools::convert_from_string<T>("11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000")), + T(boost::math::tools::convert_from_string<T>("894618213078297528685144171539831652069808216779571907213868063227837990693501860533361810841010176000000000000000000")), + T(boost::math::tools::convert_from_string<T>("71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000")), + T(boost::math::tools::convert_from_string<T>("5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000")), + T(boost::math::tools::convert_from_string<T>("475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000")), + T(boost::math::tools::convert_from_string<T>("39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000")), + T(boost::math::tools::convert_from_string<T>("3314240134565353266999387579130131288000666286242049487118846032383059131291716864129885722968716753156177920000000000000000000")), + T(boost::math::tools::convert_from_string<T>("281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000")), + T(boost::math::tools::convert_from_string<T>("24227095383672732381765523203441259715284870552429381750838764496720162249742450276789464634901319465571660595200000000000000000000")), + T(boost::math::tools::convert_from_string<T>("2107757298379527717213600518699389595229783738061356212322972511214654115727593174080683423236414793504734471782400000000000000000000")), + T(boost::math::tools::convert_from_string<T>("185482642257398439114796845645546284380220968949399346684421580986889562184028199319100141244804501828416633516851200000000000000000000")), + T(boost::math::tools::convert_from_string<T>("16507955160908461081216919262453619309839666236496541854913520707833171034378509739399912570787600662729080382999756800000000000000000000")), + T(boost::math::tools::convert_from_string<T>("1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000")), + T(boost::math::tools::convert_from_string<T>("135200152767840296255166568759495142147586866476906677791741734597153670771559994765685283954750449427751168336768008192000000000000000000000")), + T(boost::math::tools::convert_from_string<T>("12438414054641307255475324325873553077577991715875414356840239582938137710983519518443046123837041347353107486982656753664000000000000000000000")), + T(boost::math::tools::convert_from_string<T>("1156772507081641574759205162306240436214753229576413535186142281213246807121467315215203289516844845303838996289387078090752000000000000000000000")), + T(boost::math::tools::convert_from_string<T>("108736615665674308027365285256786601004186803580182872307497374434045199869417927630229109214583415458560865651202385340530688000000000000000000000")), + T(boost::math::tools::convert_from_string<T>("10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000")), + T(boost::math::tools::convert_from_string<T>("991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000")), + T(boost::math::tools::convert_from_string<T>("96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000")), + T(boost::math::tools::convert_from_string<T>("9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000")), + T(boost::math::tools::convert_from_string<T>("933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000")), + T(boost::math::tools::convert_from_string<T>("93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000")), + }}; + + return factorials[i]; +} + +template <class T> +inline T unchecked_factorial_imp(unsigned i, const mpl::int_<0>&) +{ + BOOST_STATIC_ASSERT(!boost::is_integral<T>::value); + // factorial<unsigned int>(n) is not implemented + // because it would overflow integral type T for too small n + // to be useful. Use instead a floating-point type, + // and convert to an unsigned type if essential, for example: + // unsigned int nfac = static_cast<unsigned int>(factorial<double>(n)); + // See factorial documentation for more detail. +#ifdef BOOST_NO_CXX11_THREAD_LOCAL + unchecked_factorial_initializer<T>::force_instantiate(); +#endif + static const char* const factorial_strings[] = { + "1", + "1", + "2", + "6", + "24", + "120", + "720", + "5040", + "40320", + "362880", + "3628800", + "39916800", + "479001600", + "6227020800", + "87178291200", + "1307674368000", + "20922789888000", + "355687428096000", + "6402373705728000", + "121645100408832000", + "2432902008176640000", + "51090942171709440000", + "1124000727777607680000", + "25852016738884976640000", + "620448401733239439360000", + "15511210043330985984000000", + "403291461126605635584000000", + "10888869450418352160768000000", + "304888344611713860501504000000", + "8841761993739701954543616000000", + "265252859812191058636308480000000", + "8222838654177922817725562880000000", + "263130836933693530167218012160000000", + "8683317618811886495518194401280000000", + "295232799039604140847618609643520000000", + "10333147966386144929666651337523200000000", + "371993326789901217467999448150835200000000", + "13763753091226345046315979581580902400000000", + "523022617466601111760007224100074291200000000", + "20397882081197443358640281739902897356800000000", + "815915283247897734345611269596115894272000000000", + "33452526613163807108170062053440751665152000000000", + "1405006117752879898543142606244511569936384000000000", + "60415263063373835637355132068513997507264512000000000", + "2658271574788448768043625811014615890319638528000000000", + "119622220865480194561963161495657715064383733760000000000", + "5502622159812088949850305428800254892961651752960000000000", + "258623241511168180642964355153611979969197632389120000000000", + "12413915592536072670862289047373375038521486354677760000000000", + "608281864034267560872252163321295376887552831379210240000000000", + "30414093201713378043612608166064768844377641568960512000000000000", + "1551118753287382280224243016469303211063259720016986112000000000000", + "80658175170943878571660636856403766975289505440883277824000000000000", + "4274883284060025564298013753389399649690343788366813724672000000000000", + "230843697339241380472092742683027581083278564571807941132288000000000000", + "12696403353658275925965100847566516959580321051449436762275840000000000000", + "710998587804863451854045647463724949736497978881168458687447040000000000000", + "40526919504877216755680601905432322134980384796226602145184481280000000000000", + "2350561331282878571829474910515074683828862318181142924420699914240000000000000", + "138683118545689835737939019720389406345902876772687432540821294940160000000000000", + "8320987112741390144276341183223364380754172606361245952449277696409600000000000000", + "507580213877224798800856812176625227226004528988036003099405939480985600000000000000", + "31469973260387937525653122354950764088012280797258232192163168247821107200000000000000", + "1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000", + "126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000", + "8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000", + "544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000", + "36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000", + "2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000", + "171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000", + "11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000", + "850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000", + "61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000", + "4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000", + "330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000", + "24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000", + "1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000", + "145183092028285869634070784086308284983740379224208358846781574688061991349156420080065207861248000000000000000000", + "11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000", + "894618213078297528685144171539831652069808216779571907213868063227837990693501860533361810841010176000000000000000000", + "71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000", + "5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000", + "475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000", + "39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000", + "3314240134565353266999387579130131288000666286242049487118846032383059131291716864129885722968716753156177920000000000000000000", + "281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000", + "24227095383672732381765523203441259715284870552429381750838764496720162249742450276789464634901319465571660595200000000000000000000", + "2107757298379527717213600518699389595229783738061356212322972511214654115727593174080683423236414793504734471782400000000000000000000", + "185482642257398439114796845645546284380220968949399346684421580986889562184028199319100141244804501828416633516851200000000000000000000", + "16507955160908461081216919262453619309839666236496541854913520707833171034378509739399912570787600662729080382999756800000000000000000000", + "1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000", + "135200152767840296255166568759495142147586866476906677791741734597153670771559994765685283954750449427751168336768008192000000000000000000000", + "12438414054641307255475324325873553077577991715875414356840239582938137710983519518443046123837041347353107486982656753664000000000000000000000", + "1156772507081641574759205162306240436214753229576413535186142281213246807121467315215203289516844845303838996289387078090752000000000000000000000", + "108736615665674308027365285256786601004186803580182872307497374434045199869417927630229109214583415458560865651202385340530688000000000000000000000", + "10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000", + "991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000", + "96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000", + "9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000", + "933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000", + "93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000", + }; + + static BOOST_MATH_THREAD_LOCAL T factorials[sizeof(factorial_strings) / sizeof(factorial_strings[0])]; + static BOOST_MATH_THREAD_LOCAL int digits = 0; + + int current_digits = boost::math::tools::digits<T>(); + + if(digits != current_digits) + { + digits = current_digits; + for(unsigned k = 0; k < sizeof(factorials) / sizeof(factorials[0]); ++k) + factorials[k] = static_cast<T>(boost::math::tools::convert_from_string<T>(factorial_strings[k])); + } + + return factorials[i]; +} + +template <class T> +inline T unchecked_factorial(unsigned i) +{ + typedef typename boost::math::policies::precision<T, boost::math::policies::policy<> >::type tag_type; + return unchecked_factorial_imp<T>(i, tag_type()); +} + +template <class T> +struct max_factorial +{ + BOOST_STATIC_CONSTANT(unsigned, value = 100); +}; + +#else // BOOST_MATH_NO_LEXICAL_CAST + +template <class T> +inline T unchecked_factorial(unsigned i BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T)) +{ + return 1; +} + +template <class T> +struct max_factorial +{ + BOOST_STATIC_CONSTANT(unsigned, value = 0); +}; + +#endif + +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION +template <class T> +const unsigned max_factorial<T>::value; +#endif + +} // namespace math +} // namespace boost + +#endif // BOOST_MATH_SP_UC_FACTORIALS_HPP + |