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: / usr / include / boost / math / special_functions / detail /
Filename : unchecked_factorial.hpp
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//  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>
#include <boost/math/tools/cxx03_warn.hpp>

#ifdef BOOST_MATH_HAVE_CONSTEXPR_TABLES
#include <array>
#else
#include <boost/array.hpp>
#endif

#if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
//
// This is the only way we can avoid
// warning: non-standard suffix on floating constant [-Wpedantic]
// when building with -Wall -pedantic.  Neither __extension__
// nor #pragma diagnostic ignored work :(
//
#pragma GCC system_header
#endif

namespace boost { namespace math
{
// 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,
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      0.2480035542436830599600990418569171581047e97L,
      0.1711224524281413113724683388812728390923e99L,
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      0.6123445837688608686152407038527467274078e104L,
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      0.1352001527678402962551665687594951421476e141L,
      0.1243841405464130725547532432587355307758e143L,
      0.1156772507081641574759205162306240436215e145L,
      0.1087366156656743080273652852567866010042e147L,
      0.103299784882390592625997020993947270954e149L,
      0.9916779348709496892095714015418938011582e150L,
      0.9619275968248211985332842594956369871234e152L,
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      0.9425947759838359420851623124482936749562e160L,
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      0.1081396758240290900504101305800329649721e169L,
      0.1146280563734708354534347384148349428704e171L,
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      0.1762952551090244663872161047107075788761e181L,
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      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,
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      0.26525285981219105863630848e33Q,
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      0.5230226174666011117600072241000742912e45Q,
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      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 boost::integral_constant<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 boost::integral_constant<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",
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      };

      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_imp(unsigned i, const boost::integral_constant<int, std::numeric_limits<float>::digits>&)
{
   return unchecked_factorial<float>(i);
}

template <class T>
inline T unchecked_factorial_imp(unsigned i, const boost::integral_constant<int, std::numeric_limits<double>::digits>&)
{
   return unchecked_factorial<double>(i);
}

#if DBL_MANT_DIG != LDBL_MANT_DIG
template <class T>
inline T unchecked_factorial_imp(unsigned i, const boost::integral_constant<int, LDBL_MANT_DIG>&)
{
   return unchecked_factorial<long double>(i);
}
#endif
#ifdef BOOST_MATH_USE_FLOAT128
template <class T>
inline T unchecked_factorial_imp(unsigned i, const boost::integral_constant<int, 113>&)
{
   return unchecked_factorial<BOOST_MATH_FLOAT128_TYPE>(i);
}
#endif

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());
}

#ifdef BOOST_MATH_USE_FLOAT128
#define BOOST_MATH_DETAIL_FLOAT128_MAX_FACTORIAL : std::numeric_limits<T>::digits == 113 ? max_factorial<BOOST_MATH_FLOAT128_TYPE>::value
#else
#define BOOST_MATH_DETAIL_FLOAT128_MAX_FACTORIAL
#endif

template <class T>
struct max_factorial
{
   BOOST_STATIC_CONSTANT(unsigned, value = 
      std::numeric_limits<T>::digits == std::numeric_limits<float>::digits ? max_factorial<float>::value 
      : std::numeric_limits<T>::digits == std::numeric_limits<double>::digits ? max_factorial<double>::value 
      : std::numeric_limits<T>::digits == std::numeric_limits<long double>::digits ? max_factorial<long double>::value 
      BOOST_MATH_DETAIL_FLOAT128_MAX_FACTORIAL
      : 100);
};

#undef BOOST_MATH_DETAIL_FLOAT128_MAX_FACTORIAL

#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