factorial.h

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/****************************************************************************
* VCGLib                                                            o o     *
* Visual and Computer Graphics Library                            o     o   *
*                                                                _   O  _   *
* Copyright(C) 2006                                                \/)\/    *
* Visual Computing Lab                                            /\/|      *
* ISTI - Italian National Research Council                           |      *
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* This program is free software; you can redistribute it and/or modify      *
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* (at your option) any later version.                                       *
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* This program is distributed in the hope that it will be useful,           *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the             *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt)          *
* for more details.                                                         *
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****************************************************************************/

/****************************************************************************

$Log$

****************************************************************************/

#ifndef __VCGLIB_FACTORIAL_H
#define __VCGLIB_FACTORIAL_H

namespace vcg{
namespace math{

template <typename ScalarType>
ScalarType factorial_table(unsigned i);

template <>
long double factorial_table <long double> (unsigned i)
{
        static const long double factorials[] = 
        {
                  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 <>
double factorial_table <double> (unsigned i)
{
        return static_cast<double>(factorial_table<long double>(i));
}

template <>
float factorial_table <float> (unsigned i)
{
        static const float factorials[] =
        {
                1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0, 3628800.0,
            39916800.0, 479001600.0, 6227020800.0, 87178291200.0, 1307674368000.0,
            20922789888000.0, 355687428096000.0, 6402373705728000.0, 121645100408832000.0,
            0.243290200817664e19, 0.5109094217170944e20, 0.112400072777760768e22,
            0.2585201673888497664e23, 0.62044840173323943936e24,
            0.15511210043330985984e26, 0.403291461126605635584e27,
            0.10888869450418352160768e29, 0.304888344611713860501504e30,
            0.8841761993739701954543616e31, 0.26525285981219105863630848e33,
            0.822283865417792281772556288e34, 0.26313083693369353016721801216e36,
            0.868331761881188649551819440128e37, 0.29523279903960414084761860964352e39,
        };
        
        return factorials[i];
}

template <>
int factorial_table<int> (unsigned i)
{
        return static_cast<int>(factorial_table<float>(i));
}

template <typename ScalarType>
ScalarType factorial_table(unsigned i)
{
        return static_cast<ScalarType>(factorial_table<double>(i));
}


template <typename ScalarType>
struct MAX_FACTORIAL
{
        enum {value};
};

template <> struct MAX_FACTORIAL<short>                 {enum {value = 7};};
template <> struct MAX_FACTORIAL<float>                 {enum {value = 34};};
template <> struct MAX_FACTORIAL<int>                   {enum {value = 34};};
template <> struct MAX_FACTORIAL<double>                {enum {value = 170};};
template <> struct MAX_FACTORIAL<long double>   {enum {value = 170};};


template <typename ScalarType>
ScalarType Factorial(unsigned i)
{
        assert (i <= MAX_FACTORIAL<ScalarType>::value );
        return factorial_table<ScalarType>(i);
}

}} //namespace vcg::math

#endif