1 | // 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_SP_UC_FACTORIALS_HPP |
7 | #define BOOST_MATH_SP_UC_FACTORIALS_HPP |
8 | |
9 | #ifdef _MSC_VER |
10 | #pragma once |
11 | #endif |
12 | |
13 | #ifdef BOOST_MSVC |
14 | #pragma warning(push) // Temporary until lexical cast fixed. |
15 | #pragma warning(disable: 4127 4701) |
16 | #endif |
17 | #ifndef BOOST_MATH_NO_LEXICAL_CAST |
18 | #include <boost/lexical_cast.hpp> |
19 | #endif |
20 | #ifdef BOOST_MSVC |
21 | #pragma warning(pop) |
22 | #endif |
23 | #include <cmath> |
24 | #include <boost/math/special_functions/math_fwd.hpp> |
25 | #include <boost/math/tools/cxx03_warn.hpp> |
26 | |
27 | #ifdef BOOST_MATH_HAVE_CONSTEXPR_TABLES |
28 | #include <array> |
29 | #else |
30 | #include <boost/array.hpp> |
31 | #endif |
32 | |
33 | #if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128) |
34 | // |
35 | // This is the only way we can avoid |
36 | // warning: non-standard suffix on floating constant [-Wpedantic] |
37 | // when building with -Wall -pedantic. Neither __extension__ |
38 | // nor #pragma diagnostic ignored work :( |
39 | // |
40 | #pragma GCC system_header |
41 | #endif |
42 | |
43 | namespace boost { namespace math |
44 | { |
45 | // Forward declarations: |
46 | template <class T> |
47 | struct max_factorial; |
48 | |
49 | // Definitions: |
50 | template <> |
51 | inline BOOST_MATH_CONSTEXPR_TABLE_FUNCTION float unchecked_factorial<float>(unsigned i BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(float)) |
52 | { |
53 | #ifdef BOOST_MATH_HAVE_CONSTEXPR_TABLES |
54 | constexpr std::array<float, 35> factorials = { ._M_elems: { |
55 | #else |
56 | static const boost::array<float, 35> factorials = {{ |
57 | #endif |
58 | 1.0F, |
59 | 1.0F, |
60 | 2.0F, |
61 | 6.0F, |
62 | 24.0F, |
63 | 120.0F, |
64 | 720.0F, |
65 | 5040.0F, |
66 | 40320.0F, |
67 | 362880.0F, |
68 | 3628800.0F, |
69 | 39916800.0F, |
70 | 479001600.0F, |
71 | 6227020800.0F, |
72 | 87178291200.0F, |
73 | 1307674368000.0F, |
74 | 20922789888000.0F, |
75 | 355687428096000.0F, |
76 | 6402373705728000.0F, |
77 | 121645100408832000.0F, |
78 | 0.243290200817664e19F, |
79 | 0.5109094217170944e20F, |
80 | 0.112400072777760768e22F, |
81 | 0.2585201673888497664e23F, |
82 | 0.62044840173323943936e24F, |
83 | 0.15511210043330985984e26F, |
84 | 0.403291461126605635584e27F, |
85 | 0.10888869450418352160768e29F, |
86 | 0.304888344611713860501504e30F, |
87 | 0.8841761993739701954543616e31F, |
88 | 0.26525285981219105863630848e33F, |
89 | 0.822283865417792281772556288e34F, |
90 | 0.26313083693369353016721801216e36F, |
91 | 0.868331761881188649551819440128e37F, |
92 | 0.29523279903960414084761860964352e39F, |
93 | }}; |
94 | |
95 | return factorials[i]; |
96 | } |
97 | |
98 | template <> |
99 | struct max_factorial<float> |
100 | { |
101 | BOOST_STATIC_CONSTANT(unsigned, value = 34); |
102 | }; |
103 | |
104 | |
105 | template <> |
106 | inline BOOST_MATH_CONSTEXPR_TABLE_FUNCTION long double unchecked_factorial<long double>(unsigned i BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(long double)) |
107 | { |
108 | #ifdef BOOST_MATH_HAVE_CONSTEXPR_TABLES |
109 | constexpr std::array<long double, 171> factorials = { ._M_elems: { |
110 | #else |
111 | static const boost::array<long double, 171> factorials = {{ |
112 | #endif |
113 | 1L, |
114 | 1L, |
115 | 2L, |
116 | 6L, |
117 | 24L, |
118 | 120L, |
119 | 720L, |
120 | 5040L, |
121 | 40320L, |
122 | 362880.0L, |
123 | 3628800.0L, |
124 | 39916800.0L, |
125 | 479001600.0L, |
126 | 6227020800.0L, |
127 | 87178291200.0L, |
128 | 1307674368000.0L, |
129 | 20922789888000.0L, |
130 | 355687428096000.0L, |
131 | 6402373705728000.0L, |
132 | 121645100408832000.0L, |
133 | 0.243290200817664e19L, |
134 | 0.5109094217170944e20L, |
135 | 0.112400072777760768e22L, |
136 | 0.2585201673888497664e23L, |
137 | 0.62044840173323943936e24L, |
138 | 0.15511210043330985984e26L, |
139 | 0.403291461126605635584e27L, |
140 | 0.10888869450418352160768e29L, |
141 | 0.304888344611713860501504e30L, |
142 | 0.8841761993739701954543616e31L, |
143 | 0.26525285981219105863630848e33L, |
144 | 0.822283865417792281772556288e34L, |
145 | 0.26313083693369353016721801216e36L, |
146 | 0.868331761881188649551819440128e37L, |
147 | 0.29523279903960414084761860964352e39L, |
148 | 0.103331479663861449296666513375232e41L, |
149 | 0.3719933267899012174679994481508352e42L, |
150 | 0.137637530912263450463159795815809024e44L, |
151 | 0.5230226174666011117600072241000742912e45L, |
152 | 0.203978820811974433586402817399028973568e47L, |
153 | 0.815915283247897734345611269596115894272e48L, |
154 | 0.3345252661316380710817006205344075166515e50L, |
155 | 0.1405006117752879898543142606244511569936e52L, |
156 | 0.6041526306337383563735513206851399750726e53L, |
157 | 0.265827157478844876804362581101461589032e55L, |
158 | 0.1196222208654801945619631614956577150644e57L, |
159 | 0.5502622159812088949850305428800254892962e58L, |
160 | 0.2586232415111681806429643551536119799692e60L, |
161 | 0.1241391559253607267086228904737337503852e62L, |
162 | 0.6082818640342675608722521633212953768876e63L, |
163 | 0.3041409320171337804361260816606476884438e65L, |
164 | 0.1551118753287382280224243016469303211063e67L, |
165 | 0.8065817517094387857166063685640376697529e68L, |
166 | 0.427488328406002556429801375338939964969e70L, |
167 | 0.2308436973392413804720927426830275810833e72L, |
168 | 0.1269640335365827592596510084756651695958e74L, |
169 | 0.7109985878048634518540456474637249497365e75L, |
170 | 0.4052691950487721675568060190543232213498e77L, |
171 | 0.2350561331282878571829474910515074683829e79L, |
172 | 0.1386831185456898357379390197203894063459e81L, |
173 | 0.8320987112741390144276341183223364380754e82L, |
174 | 0.507580213877224798800856812176625227226e84L, |
175 | 0.3146997326038793752565312235495076408801e86L, |
176 | 0.1982608315404440064116146708361898137545e88L, |
177 | 0.1268869321858841641034333893351614808029e90L, |
178 | 0.8247650592082470666723170306785496252186e91L, |
179 | 0.5443449390774430640037292402478427526443e93L, |
180 | 0.3647111091818868528824985909660546442717e95L, |
181 | 0.2480035542436830599600990418569171581047e97L, |
182 | 0.1711224524281413113724683388812728390923e99L, |
183 | 0.1197857166996989179607278372168909873646e101L, |
184 | 0.8504785885678623175211676442399260102886e102L, |
185 | 0.6123445837688608686152407038527467274078e104L, |
186 | 0.4470115461512684340891257138125051110077e106L, |
187 | 0.3307885441519386412259530282212537821457e108L, |
188 | 0.2480914081139539809194647711659403366093e110L, |
189 | 0.188549470166605025498793226086114655823e112L, |
190 | 0.1451830920282858696340707840863082849837e114L, |
191 | 0.1132428117820629783145752115873204622873e116L, |
192 | 0.8946182130782975286851441715398316520698e117L, |
193 | 0.7156945704626380229481153372318653216558e119L, |
194 | 0.5797126020747367985879734231578109105412e121L, |
195 | 0.4753643337012841748421382069894049466438e123L, |
196 | 0.3945523969720658651189747118012061057144e125L, |
197 | 0.3314240134565353266999387579130131288001e127L, |
198 | 0.2817104114380550276949479442260611594801e129L, |
199 | 0.2422709538367273238176552320344125971528e131L, |
200 | 0.210775729837952771721360051869938959523e133L, |
201 | 0.1854826422573984391147968456455462843802e135L, |
202 | 0.1650795516090846108121691926245361930984e137L, |
203 | 0.1485715964481761497309522733620825737886e139L, |
204 | 0.1352001527678402962551665687594951421476e141L, |
205 | 0.1243841405464130725547532432587355307758e143L, |
206 | 0.1156772507081641574759205162306240436215e145L, |
207 | 0.1087366156656743080273652852567866010042e147L, |
208 | 0.103299784882390592625997020993947270954e149L, |
209 | 0.9916779348709496892095714015418938011582e150L, |
210 | 0.9619275968248211985332842594956369871234e152L, |
211 | 0.942689044888324774562618574305724247381e154L, |
212 | 0.9332621544394415268169923885626670049072e156L, |
213 | 0.9332621544394415268169923885626670049072e158L, |
214 | 0.9425947759838359420851623124482936749562e160L, |
215 | 0.9614466715035126609268655586972595484554e162L, |
216 | 0.990290071648618040754671525458177334909e164L, |
217 | 0.1029901674514562762384858386476504428305e167L, |
218 | 0.1081396758240290900504101305800329649721e169L, |
219 | 0.1146280563734708354534347384148349428704e171L, |
220 | 0.1226520203196137939351751701038733888713e173L, |
221 | 0.132464181945182897449989183712183259981e175L, |
222 | 0.1443859583202493582204882102462797533793e177L, |
223 | 0.1588245541522742940425370312709077287172e179L, |
224 | 0.1762952551090244663872161047107075788761e181L, |
225 | 0.1974506857221074023536820372759924883413e183L, |
226 | 0.2231192748659813646596607021218715118256e185L, |
227 | 0.2543559733472187557120132004189335234812e187L, |
228 | 0.2925093693493015690688151804817735520034e189L, |
229 | 0.339310868445189820119825609358857320324e191L, |
230 | 0.396993716080872089540195962949863064779e193L, |
231 | 0.4684525849754290656574312362808384164393e195L, |
232 | 0.5574585761207605881323431711741977155627e197L, |
233 | 0.6689502913449127057588118054090372586753e199L, |
234 | 0.8094298525273443739681622845449350829971e201L, |
235 | 0.9875044200833601362411579871448208012564e203L, |
236 | 0.1214630436702532967576624324188129585545e206L, |
237 | 0.1506141741511140879795014161993280686076e208L, |
238 | 0.1882677176888926099743767702491600857595e210L, |
239 | 0.237217324288004688567714730513941708057e212L, |
240 | 0.3012660018457659544809977077527059692324e214L, |
241 | 0.3856204823625804217356770659234636406175e216L, |
242 | 0.4974504222477287440390234150412680963966e218L, |
243 | 0.6466855489220473672507304395536485253155e220L, |
244 | 0.8471580690878820510984568758152795681634e222L, |
245 | 0.1118248651196004307449963076076169029976e225L, |
246 | 0.1487270706090685728908450891181304809868e227L, |
247 | 0.1992942746161518876737324194182948445223e229L, |
248 | 0.269047270731805048359538766214698040105e231L, |
249 | 0.3659042881952548657689727220519893345429e233L, |
250 | 0.5012888748274991661034926292112253883237e235L, |
251 | 0.6917786472619488492228198283114910358867e237L, |
252 | 0.9615723196941089004197195613529725398826e239L, |
253 | 0.1346201247571752460587607385894161555836e242L, |
254 | 0.1898143759076170969428526414110767793728e244L, |
255 | 0.2695364137888162776588507508037290267094e246L, |
256 | 0.3854370717180072770521565736493325081944e248L, |
257 | 0.5550293832739304789551054660550388118e250L, |
258 | 0.80479260574719919448490292577980627711e252L, |
259 | 0.1174997204390910823947958271638517164581e255L, |
260 | 0.1727245890454638911203498659308620231933e257L, |
261 | 0.2556323917872865588581178015776757943262e259L, |
262 | 0.380892263763056972698595524350736933546e261L, |
263 | 0.571338395644585459047893286526105400319e263L, |
264 | 0.8627209774233240431623188626544191544816e265L, |
265 | 0.1311335885683452545606724671234717114812e268L, |
266 | 0.2006343905095682394778288746989117185662e270L, |
267 | 0.308976961384735088795856467036324046592e272L, |
268 | 0.4789142901463393876335775239063022722176e274L, |
269 | 0.7471062926282894447083809372938315446595e276L, |
270 | 0.1172956879426414428192158071551315525115e279L, |
271 | 0.1853271869493734796543609753051078529682e281L, |
272 | 0.2946702272495038326504339507351214862195e283L, |
273 | 0.4714723635992061322406943211761943779512e285L, |
274 | 0.7590705053947218729075178570936729485014e287L, |
275 | 0.1229694218739449434110178928491750176572e290L, |
276 | 0.2004401576545302577599591653441552787813e292L, |
277 | 0.3287218585534296227263330311644146572013e294L, |
278 | 0.5423910666131588774984495014212841843822e296L, |
279 | 0.9003691705778437366474261723593317460744e298L, |
280 | 0.1503616514864999040201201707840084015944e301L, |
281 | 0.2526075744973198387538018869171341146786e303L, |
282 | 0.4269068009004705274939251888899566538069e305L, |
283 | 0.7257415615307998967396728211129263114717e307L, |
284 | }}; |
285 | |
286 | return factorials[i]; |
287 | } |
288 | |
289 | template <> |
290 | struct max_factorial<long double> |
291 | { |
292 | BOOST_STATIC_CONSTANT(unsigned, value = 170); |
293 | }; |
294 | |
295 | #ifdef BOOST_MATH_USE_FLOAT128 |
296 | |
297 | template <> |
298 | inline BOOST_MATH_CONSTEXPR_TABLE_FUNCTION BOOST_MATH_FLOAT128_TYPE unchecked_factorial<BOOST_MATH_FLOAT128_TYPE>(unsigned i) |
299 | { |
300 | #ifdef BOOST_MATH_HAVE_CONSTEXPR_TABLES |
301 | constexpr std::array<BOOST_MATH_FLOAT128_TYPE, 171> factorials = { { |
302 | #else |
303 | static const boost::array<BOOST_MATH_FLOAT128_TYPE, 171> factorials = { { |
304 | #endif |
305 | 1, |
306 | 1, |
307 | 2, |
308 | 6, |
309 | 24, |
310 | 120, |
311 | 720, |
312 | 5040, |
313 | 40320, |
314 | 362880.0Q, |
315 | 3628800.0Q, |
316 | 39916800.0Q, |
317 | 479001600.0Q, |
318 | 6227020800.0Q, |
319 | 87178291200.0Q, |
320 | 1307674368000.0Q, |
321 | 20922789888000.0Q, |
322 | 355687428096000.0Q, |
323 | 6402373705728000.0Q, |
324 | 121645100408832000.0Q, |
325 | 0.243290200817664e19Q, |
326 | 0.5109094217170944e20Q, |
327 | 0.112400072777760768e22Q, |
328 | 0.2585201673888497664e23Q, |
329 | 0.62044840173323943936e24Q, |
330 | 0.15511210043330985984e26Q, |
331 | 0.403291461126605635584e27Q, |
332 | 0.10888869450418352160768e29Q, |
333 | 0.304888344611713860501504e30Q, |
334 | 0.8841761993739701954543616e31Q, |
335 | 0.26525285981219105863630848e33Q, |
336 | 0.822283865417792281772556288e34Q, |
337 | 0.26313083693369353016721801216e36Q, |
338 | 0.868331761881188649551819440128e37Q, |
339 | 0.29523279903960414084761860964352e39Q, |
340 | 0.103331479663861449296666513375232e41Q, |
341 | 0.3719933267899012174679994481508352e42Q, |
342 | 0.137637530912263450463159795815809024e44Q, |
343 | 0.5230226174666011117600072241000742912e45Q, |
344 | 0.203978820811974433586402817399028973568e47Q, |
345 | 0.815915283247897734345611269596115894272e48Q, |
346 | 0.3345252661316380710817006205344075166515e50Q, |
347 | 0.1405006117752879898543142606244511569936e52Q, |
348 | 0.6041526306337383563735513206851399750726e53Q, |
349 | 0.265827157478844876804362581101461589032e55Q, |
350 | 0.1196222208654801945619631614956577150644e57Q, |
351 | 0.5502622159812088949850305428800254892962e58Q, |
352 | 0.2586232415111681806429643551536119799692e60Q, |
353 | 0.1241391559253607267086228904737337503852e62Q, |
354 | 0.6082818640342675608722521633212953768876e63Q, |
355 | 0.3041409320171337804361260816606476884438e65Q, |
356 | 0.1551118753287382280224243016469303211063e67Q, |
357 | 0.8065817517094387857166063685640376697529e68Q, |
358 | 0.427488328406002556429801375338939964969e70Q, |
359 | 0.2308436973392413804720927426830275810833e72Q, |
360 | 0.1269640335365827592596510084756651695958e74Q, |
361 | 0.7109985878048634518540456474637249497365e75Q, |
362 | 0.4052691950487721675568060190543232213498e77Q, |
363 | 0.2350561331282878571829474910515074683829e79Q, |
364 | 0.1386831185456898357379390197203894063459e81Q, |
365 | 0.8320987112741390144276341183223364380754e82Q, |
366 | 0.507580213877224798800856812176625227226e84Q, |
367 | 0.3146997326038793752565312235495076408801e86Q, |
368 | 0.1982608315404440064116146708361898137545e88Q, |
369 | 0.1268869321858841641034333893351614808029e90Q, |
370 | 0.8247650592082470666723170306785496252186e91Q, |
371 | 0.5443449390774430640037292402478427526443e93Q, |
372 | 0.3647111091818868528824985909660546442717e95Q, |
373 | 0.2480035542436830599600990418569171581047e97Q, |
374 | 0.1711224524281413113724683388812728390923e99Q, |
375 | 0.1197857166996989179607278372168909873646e101Q, |
376 | 0.8504785885678623175211676442399260102886e102Q, |
377 | 0.6123445837688608686152407038527467274078e104Q, |
378 | 0.4470115461512684340891257138125051110077e106Q, |
379 | 0.3307885441519386412259530282212537821457e108Q, |
380 | 0.2480914081139539809194647711659403366093e110Q, |
381 | 0.188549470166605025498793226086114655823e112Q, |
382 | 0.1451830920282858696340707840863082849837e114Q, |
383 | 0.1132428117820629783145752115873204622873e116Q, |
384 | 0.8946182130782975286851441715398316520698e117Q, |
385 | 0.7156945704626380229481153372318653216558e119Q, |
386 | 0.5797126020747367985879734231578109105412e121Q, |
387 | 0.4753643337012841748421382069894049466438e123Q, |
388 | 0.3945523969720658651189747118012061057144e125Q, |
389 | 0.3314240134565353266999387579130131288001e127Q, |
390 | 0.2817104114380550276949479442260611594801e129Q, |
391 | 0.2422709538367273238176552320344125971528e131Q, |
392 | 0.210775729837952771721360051869938959523e133Q, |
393 | 0.1854826422573984391147968456455462843802e135Q, |
394 | 0.1650795516090846108121691926245361930984e137Q, |
395 | 0.1485715964481761497309522733620825737886e139Q, |
396 | 0.1352001527678402962551665687594951421476e141Q, |
397 | 0.1243841405464130725547532432587355307758e143Q, |
398 | 0.1156772507081641574759205162306240436215e145Q, |
399 | 0.1087366156656743080273652852567866010042e147Q, |
400 | 0.103299784882390592625997020993947270954e149Q, |
401 | 0.9916779348709496892095714015418938011582e150Q, |
402 | 0.9619275968248211985332842594956369871234e152Q, |
403 | 0.942689044888324774562618574305724247381e154Q, |
404 | 0.9332621544394415268169923885626670049072e156Q, |
405 | 0.9332621544394415268169923885626670049072e158Q, |
406 | 0.9425947759838359420851623124482936749562e160Q, |
407 | 0.9614466715035126609268655586972595484554e162Q, |
408 | 0.990290071648618040754671525458177334909e164Q, |
409 | 0.1029901674514562762384858386476504428305e167Q, |
410 | 0.1081396758240290900504101305800329649721e169Q, |
411 | 0.1146280563734708354534347384148349428704e171Q, |
412 | 0.1226520203196137939351751701038733888713e173Q, |
413 | 0.132464181945182897449989183712183259981e175Q, |
414 | 0.1443859583202493582204882102462797533793e177Q, |
415 | 0.1588245541522742940425370312709077287172e179Q, |
416 | 0.1762952551090244663872161047107075788761e181Q, |
417 | 0.1974506857221074023536820372759924883413e183Q, |
418 | 0.2231192748659813646596607021218715118256e185Q, |
419 | 0.2543559733472187557120132004189335234812e187Q, |
420 | 0.2925093693493015690688151804817735520034e189Q, |
421 | 0.339310868445189820119825609358857320324e191Q, |
422 | 0.396993716080872089540195962949863064779e193Q, |
423 | 0.4684525849754290656574312362808384164393e195Q, |
424 | 0.5574585761207605881323431711741977155627e197Q, |
425 | 0.6689502913449127057588118054090372586753e199Q, |
426 | 0.8094298525273443739681622845449350829971e201Q, |
427 | 0.9875044200833601362411579871448208012564e203Q, |
428 | 0.1214630436702532967576624324188129585545e206Q, |
429 | 0.1506141741511140879795014161993280686076e208Q, |
430 | 0.1882677176888926099743767702491600857595e210Q, |
431 | 0.237217324288004688567714730513941708057e212Q, |
432 | 0.3012660018457659544809977077527059692324e214Q, |
433 | 0.3856204823625804217356770659234636406175e216Q, |
434 | 0.4974504222477287440390234150412680963966e218Q, |
435 | 0.6466855489220473672507304395536485253155e220Q, |
436 | 0.8471580690878820510984568758152795681634e222Q, |
437 | 0.1118248651196004307449963076076169029976e225Q, |
438 | 0.1487270706090685728908450891181304809868e227Q, |
439 | 0.1992942746161518876737324194182948445223e229Q, |
440 | 0.269047270731805048359538766214698040105e231Q, |
441 | 0.3659042881952548657689727220519893345429e233Q, |
442 | 0.5012888748274991661034926292112253883237e235Q, |
443 | 0.6917786472619488492228198283114910358867e237Q, |
444 | 0.9615723196941089004197195613529725398826e239Q, |
445 | 0.1346201247571752460587607385894161555836e242Q, |
446 | 0.1898143759076170969428526414110767793728e244Q, |
447 | 0.2695364137888162776588507508037290267094e246Q, |
448 | 0.3854370717180072770521565736493325081944e248Q, |
449 | 0.5550293832739304789551054660550388118e250Q, |
450 | 0.80479260574719919448490292577980627711e252Q, |
451 | 0.1174997204390910823947958271638517164581e255Q, |
452 | 0.1727245890454638911203498659308620231933e257Q, |
453 | 0.2556323917872865588581178015776757943262e259Q, |
454 | 0.380892263763056972698595524350736933546e261Q, |
455 | 0.571338395644585459047893286526105400319e263Q, |
456 | 0.8627209774233240431623188626544191544816e265Q, |
457 | 0.1311335885683452545606724671234717114812e268Q, |
458 | 0.2006343905095682394778288746989117185662e270Q, |
459 | 0.308976961384735088795856467036324046592e272Q, |
460 | 0.4789142901463393876335775239063022722176e274Q, |
461 | 0.7471062926282894447083809372938315446595e276Q, |
462 | 0.1172956879426414428192158071551315525115e279Q, |
463 | 0.1853271869493734796543609753051078529682e281Q, |
464 | 0.2946702272495038326504339507351214862195e283Q, |
465 | 0.4714723635992061322406943211761943779512e285Q, |
466 | 0.7590705053947218729075178570936729485014e287Q, |
467 | 0.1229694218739449434110178928491750176572e290Q, |
468 | 0.2004401576545302577599591653441552787813e292Q, |
469 | 0.3287218585534296227263330311644146572013e294Q, |
470 | 0.5423910666131588774984495014212841843822e296Q, |
471 | 0.9003691705778437366474261723593317460744e298Q, |
472 | 0.1503616514864999040201201707840084015944e301Q, |
473 | 0.2526075744973198387538018869171341146786e303Q, |
474 | 0.4269068009004705274939251888899566538069e305Q, |
475 | 0.7257415615307998967396728211129263114717e307Q, |
476 | } }; |
477 | |
478 | return factorials[i]; |
479 | } |
480 | |
481 | template <> |
482 | struct max_factorial<BOOST_MATH_FLOAT128_TYPE> |
483 | { |
484 | BOOST_STATIC_CONSTANT(unsigned, value = 170); |
485 | }; |
486 | |
487 | #endif |
488 | |
489 | template <> |
490 | inline BOOST_MATH_CONSTEXPR_TABLE_FUNCTION double unchecked_factorial<double>(unsigned i BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(double)) |
491 | { |
492 | return static_cast<double>(boost::math::unchecked_factorial<long double>(i)); |
493 | } |
494 | |
495 | template <> |
496 | struct max_factorial<double> |
497 | { |
498 | BOOST_STATIC_CONSTANT(unsigned, |
499 | value = ::boost::math::max_factorial<long double>::value); |
500 | }; |
501 | |
502 | #ifndef BOOST_MATH_NO_LEXICAL_CAST |
503 | |
504 | template <class T> |
505 | struct unchecked_factorial_initializer |
506 | { |
507 | struct init |
508 | { |
509 | init() |
510 | { |
511 | boost::math::unchecked_factorial<T>(3); |
512 | } |
513 | void force_instantiate()const {} |
514 | }; |
515 | static const init initializer; |
516 | static void force_instantiate() |
517 | { |
518 | initializer.force_instantiate(); |
519 | } |
520 | }; |
521 | |
522 | template <class T> |
523 | const typename unchecked_factorial_initializer<T>::init unchecked_factorial_initializer<T>::initializer; |
524 | |
525 | |
526 | template <class T, int N> |
527 | inline T unchecked_factorial_imp(unsigned i, const boost::integral_constant<int, N>&) |
528 | { |
529 | BOOST_STATIC_ASSERT(!boost::is_integral<T>::value); |
530 | // factorial<unsigned int>(n) is not implemented |
531 | // because it would overflow integral type T for too small n |
532 | // to be useful. Use instead a floating-point type, |
533 | // and convert to an unsigned type if essential, for example: |
534 | // unsigned int nfac = static_cast<unsigned int>(factorial<double>(n)); |
535 | // See factorial documentation for more detail. |
536 | |
537 | unchecked_factorial_initializer<T>::force_instantiate(); |
538 | |
539 | static const boost::array<T, 101> factorials = {{ |
540 | T(boost::math::tools::convert_from_string<T>("1" )), |
541 | T(boost::math::tools::convert_from_string<T>("1" )), |
542 | T(boost::math::tools::convert_from_string<T>("2" )), |
543 | T(boost::math::tools::convert_from_string<T>("6" )), |
544 | T(boost::math::tools::convert_from_string<T>("24" )), |
545 | T(boost::math::tools::convert_from_string<T>("120" )), |
546 | T(boost::math::tools::convert_from_string<T>("720" )), |
547 | T(boost::math::tools::convert_from_string<T>("5040" )), |
548 | T(boost::math::tools::convert_from_string<T>("40320" )), |
549 | T(boost::math::tools::convert_from_string<T>("362880" )), |
550 | T(boost::math::tools::convert_from_string<T>("3628800" )), |
551 | T(boost::math::tools::convert_from_string<T>("39916800" )), |
552 | T(boost::math::tools::convert_from_string<T>("479001600" )), |
553 | T(boost::math::tools::convert_from_string<T>("6227020800" )), |
554 | T(boost::math::tools::convert_from_string<T>("87178291200" )), |
555 | T(boost::math::tools::convert_from_string<T>("1307674368000" )), |
556 | T(boost::math::tools::convert_from_string<T>("20922789888000" )), |
557 | T(boost::math::tools::convert_from_string<T>("355687428096000" )), |
558 | T(boost::math::tools::convert_from_string<T>("6402373705728000" )), |
559 | T(boost::math::tools::convert_from_string<T>("121645100408832000" )), |
560 | T(boost::math::tools::convert_from_string<T>("2432902008176640000" )), |
561 | T(boost::math::tools::convert_from_string<T>("51090942171709440000" )), |
562 | T(boost::math::tools::convert_from_string<T>("1124000727777607680000" )), |
563 | T(boost::math::tools::convert_from_string<T>("25852016738884976640000" )), |
564 | T(boost::math::tools::convert_from_string<T>("620448401733239439360000" )), |
565 | T(boost::math::tools::convert_from_string<T>("15511210043330985984000000" )), |
566 | T(boost::math::tools::convert_from_string<T>("403291461126605635584000000" )), |
567 | T(boost::math::tools::convert_from_string<T>("10888869450418352160768000000" )), |
568 | T(boost::math::tools::convert_from_string<T>("304888344611713860501504000000" )), |
569 | T(boost::math::tools::convert_from_string<T>("8841761993739701954543616000000" )), |
570 | T(boost::math::tools::convert_from_string<T>("265252859812191058636308480000000" )), |
571 | T(boost::math::tools::convert_from_string<T>("8222838654177922817725562880000000" )), |
572 | T(boost::math::tools::convert_from_string<T>("263130836933693530167218012160000000" )), |
573 | T(boost::math::tools::convert_from_string<T>("8683317618811886495518194401280000000" )), |
574 | T(boost::math::tools::convert_from_string<T>("295232799039604140847618609643520000000" )), |
575 | T(boost::math::tools::convert_from_string<T>("10333147966386144929666651337523200000000" )), |
576 | T(boost::math::tools::convert_from_string<T>("371993326789901217467999448150835200000000" )), |
577 | T(boost::math::tools::convert_from_string<T>("13763753091226345046315979581580902400000000" )), |
578 | T(boost::math::tools::convert_from_string<T>("523022617466601111760007224100074291200000000" )), |
579 | T(boost::math::tools::convert_from_string<T>("20397882081197443358640281739902897356800000000" )), |
580 | T(boost::math::tools::convert_from_string<T>("815915283247897734345611269596115894272000000000" )), |
581 | T(boost::math::tools::convert_from_string<T>("33452526613163807108170062053440751665152000000000" )), |
582 | T(boost::math::tools::convert_from_string<T>("1405006117752879898543142606244511569936384000000000" )), |
583 | T(boost::math::tools::convert_from_string<T>("60415263063373835637355132068513997507264512000000000" )), |
584 | T(boost::math::tools::convert_from_string<T>("2658271574788448768043625811014615890319638528000000000" )), |
585 | T(boost::math::tools::convert_from_string<T>("119622220865480194561963161495657715064383733760000000000" )), |
586 | T(boost::math::tools::convert_from_string<T>("5502622159812088949850305428800254892961651752960000000000" )), |
587 | T(boost::math::tools::convert_from_string<T>("258623241511168180642964355153611979969197632389120000000000" )), |
588 | T(boost::math::tools::convert_from_string<T>("12413915592536072670862289047373375038521486354677760000000000" )), |
589 | T(boost::math::tools::convert_from_string<T>("608281864034267560872252163321295376887552831379210240000000000" )), |
590 | T(boost::math::tools::convert_from_string<T>("30414093201713378043612608166064768844377641568960512000000000000" )), |
591 | T(boost::math::tools::convert_from_string<T>("1551118753287382280224243016469303211063259720016986112000000000000" )), |
592 | T(boost::math::tools::convert_from_string<T>("80658175170943878571660636856403766975289505440883277824000000000000" )), |
593 | T(boost::math::tools::convert_from_string<T>("4274883284060025564298013753389399649690343788366813724672000000000000" )), |
594 | T(boost::math::tools::convert_from_string<T>("230843697339241380472092742683027581083278564571807941132288000000000000" )), |
595 | T(boost::math::tools::convert_from_string<T>("12696403353658275925965100847566516959580321051449436762275840000000000000" )), |
596 | T(boost::math::tools::convert_from_string<T>("710998587804863451854045647463724949736497978881168458687447040000000000000" )), |
597 | T(boost::math::tools::convert_from_string<T>("40526919504877216755680601905432322134980384796226602145184481280000000000000" )), |
598 | T(boost::math::tools::convert_from_string<T>("2350561331282878571829474910515074683828862318181142924420699914240000000000000" )), |
599 | T(boost::math::tools::convert_from_string<T>("138683118545689835737939019720389406345902876772687432540821294940160000000000000" )), |
600 | T(boost::math::tools::convert_from_string<T>("8320987112741390144276341183223364380754172606361245952449277696409600000000000000" )), |
601 | T(boost::math::tools::convert_from_string<T>("507580213877224798800856812176625227226004528988036003099405939480985600000000000000" )), |
602 | T(boost::math::tools::convert_from_string<T>("31469973260387937525653122354950764088012280797258232192163168247821107200000000000000" )), |
603 | T(boost::math::tools::convert_from_string<T>("1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000" )), |
604 | T(boost::math::tools::convert_from_string<T>("126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000" )), |
605 | T(boost::math::tools::convert_from_string<T>("8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000" )), |
606 | T(boost::math::tools::convert_from_string<T>("544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000" )), |
607 | T(boost::math::tools::convert_from_string<T>("36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000" )), |
608 | T(boost::math::tools::convert_from_string<T>("2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000" )), |
609 | T(boost::math::tools::convert_from_string<T>("171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000" )), |
610 | T(boost::math::tools::convert_from_string<T>("11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000" )), |
611 | T(boost::math::tools::convert_from_string<T>("850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000" )), |
612 | T(boost::math::tools::convert_from_string<T>("61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000" )), |
613 | T(boost::math::tools::convert_from_string<T>("4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000" )), |
614 | T(boost::math::tools::convert_from_string<T>("330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000" )), |
615 | T(boost::math::tools::convert_from_string<T>("24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000" )), |
616 | T(boost::math::tools::convert_from_string<T>("1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000" )), |
617 | T(boost::math::tools::convert_from_string<T>("145183092028285869634070784086308284983740379224208358846781574688061991349156420080065207861248000000000000000000" )), |
618 | T(boost::math::tools::convert_from_string<T>("11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000" )), |
619 | T(boost::math::tools::convert_from_string<T>("894618213078297528685144171539831652069808216779571907213868063227837990693501860533361810841010176000000000000000000" )), |
620 | T(boost::math::tools::convert_from_string<T>("71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000" )), |
621 | T(boost::math::tools::convert_from_string<T>("5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000" )), |
622 | T(boost::math::tools::convert_from_string<T>("475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000" )), |
623 | T(boost::math::tools::convert_from_string<T>("39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000" )), |
624 | T(boost::math::tools::convert_from_string<T>("3314240134565353266999387579130131288000666286242049487118846032383059131291716864129885722968716753156177920000000000000000000" )), |
625 | T(boost::math::tools::convert_from_string<T>("281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000" )), |
626 | T(boost::math::tools::convert_from_string<T>("24227095383672732381765523203441259715284870552429381750838764496720162249742450276789464634901319465571660595200000000000000000000" )), |
627 | T(boost::math::tools::convert_from_string<T>("2107757298379527717213600518699389595229783738061356212322972511214654115727593174080683423236414793504734471782400000000000000000000" )), |
628 | T(boost::math::tools::convert_from_string<T>("185482642257398439114796845645546284380220968949399346684421580986889562184028199319100141244804501828416633516851200000000000000000000" )), |
629 | T(boost::math::tools::convert_from_string<T>("16507955160908461081216919262453619309839666236496541854913520707833171034378509739399912570787600662729080382999756800000000000000000000" )), |
630 | T(boost::math::tools::convert_from_string<T>("1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000" )), |
631 | T(boost::math::tools::convert_from_string<T>("135200152767840296255166568759495142147586866476906677791741734597153670771559994765685283954750449427751168336768008192000000000000000000000" )), |
632 | T(boost::math::tools::convert_from_string<T>("12438414054641307255475324325873553077577991715875414356840239582938137710983519518443046123837041347353107486982656753664000000000000000000000" )), |
633 | T(boost::math::tools::convert_from_string<T>("1156772507081641574759205162306240436214753229576413535186142281213246807121467315215203289516844845303838996289387078090752000000000000000000000" )), |
634 | T(boost::math::tools::convert_from_string<T>("108736615665674308027365285256786601004186803580182872307497374434045199869417927630229109214583415458560865651202385340530688000000000000000000000" )), |
635 | T(boost::math::tools::convert_from_string<T>("10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000" )), |
636 | T(boost::math::tools::convert_from_string<T>("991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000" )), |
637 | T(boost::math::tools::convert_from_string<T>("96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000" )), |
638 | T(boost::math::tools::convert_from_string<T>("9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000" )), |
639 | T(boost::math::tools::convert_from_string<T>("933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000" )), |
640 | T(boost::math::tools::convert_from_string<T>("93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000" )), |
641 | }}; |
642 | |
643 | return factorials[i]; |
644 | } |
645 | |
646 | template <class T> |
647 | inline T unchecked_factorial_imp(unsigned i, const boost::integral_constant<int, 0>&) |
648 | { |
649 | BOOST_STATIC_ASSERT(!boost::is_integral<T>::value); |
650 | // factorial<unsigned int>(n) is not implemented |
651 | // because it would overflow integral type T for too small n |
652 | // to be useful. Use instead a floating-point type, |
653 | // and convert to an unsigned type if essential, for example: |
654 | // unsigned int nfac = static_cast<unsigned int>(factorial<double>(n)); |
655 | // See factorial documentation for more detail. |
656 | #ifdef BOOST_NO_CXX11_THREAD_LOCAL |
657 | unchecked_factorial_initializer<T>::force_instantiate(); |
658 | #endif |
659 | static const char* const factorial_strings[] = { |
660 | "1" , |
661 | "1" , |
662 | "2" , |
663 | "6" , |
664 | "24" , |
665 | "120" , |
666 | "720" , |
667 | "5040" , |
668 | "40320" , |
669 | "362880" , |
670 | "3628800" , |
671 | "39916800" , |
672 | "479001600" , |
673 | "6227020800" , |
674 | "87178291200" , |
675 | "1307674368000" , |
676 | "20922789888000" , |
677 | "355687428096000" , |
678 | "6402373705728000" , |
679 | "121645100408832000" , |
680 | "2432902008176640000" , |
681 | "51090942171709440000" , |
682 | "1124000727777607680000" , |
683 | "25852016738884976640000" , |
684 | "620448401733239439360000" , |
685 | "15511210043330985984000000" , |
686 | "403291461126605635584000000" , |
687 | "10888869450418352160768000000" , |
688 | "304888344611713860501504000000" , |
689 | "8841761993739701954543616000000" , |
690 | "265252859812191058636308480000000" , |
691 | "8222838654177922817725562880000000" , |
692 | "263130836933693530167218012160000000" , |
693 | "8683317618811886495518194401280000000" , |
694 | "295232799039604140847618609643520000000" , |
695 | "10333147966386144929666651337523200000000" , |
696 | "371993326789901217467999448150835200000000" , |
697 | "13763753091226345046315979581580902400000000" , |
698 | "523022617466601111760007224100074291200000000" , |
699 | "20397882081197443358640281739902897356800000000" , |
700 | "815915283247897734345611269596115894272000000000" , |
701 | "33452526613163807108170062053440751665152000000000" , |
702 | "1405006117752879898543142606244511569936384000000000" , |
703 | "60415263063373835637355132068513997507264512000000000" , |
704 | "2658271574788448768043625811014615890319638528000000000" , |
705 | "119622220865480194561963161495657715064383733760000000000" , |
706 | "5502622159812088949850305428800254892961651752960000000000" , |
707 | "258623241511168180642964355153611979969197632389120000000000" , |
708 | "12413915592536072670862289047373375038521486354677760000000000" , |
709 | "608281864034267560872252163321295376887552831379210240000000000" , |
710 | "30414093201713378043612608166064768844377641568960512000000000000" , |
711 | "1551118753287382280224243016469303211063259720016986112000000000000" , |
712 | "80658175170943878571660636856403766975289505440883277824000000000000" , |
713 | "4274883284060025564298013753389399649690343788366813724672000000000000" , |
714 | "230843697339241380472092742683027581083278564571807941132288000000000000" , |
715 | "12696403353658275925965100847566516959580321051449436762275840000000000000" , |
716 | "710998587804863451854045647463724949736497978881168458687447040000000000000" , |
717 | "40526919504877216755680601905432322134980384796226602145184481280000000000000" , |
718 | "2350561331282878571829474910515074683828862318181142924420699914240000000000000" , |
719 | "138683118545689835737939019720389406345902876772687432540821294940160000000000000" , |
720 | "8320987112741390144276341183223364380754172606361245952449277696409600000000000000" , |
721 | "507580213877224798800856812176625227226004528988036003099405939480985600000000000000" , |
722 | "31469973260387937525653122354950764088012280797258232192163168247821107200000000000000" , |
723 | "1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000" , |
724 | "126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000" , |
725 | "8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000" , |
726 | "544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000" , |
727 | "36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000" , |
728 | "2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000" , |
729 | "171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000" , |
730 | "11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000" , |
731 | "850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000" , |
732 | "61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000" , |
733 | "4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000" , |
734 | "330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000" , |
735 | "24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000" , |
736 | "1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000" , |
737 | "145183092028285869634070784086308284983740379224208358846781574688061991349156420080065207861248000000000000000000" , |
738 | "11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000" , |
739 | "894618213078297528685144171539831652069808216779571907213868063227837990693501860533361810841010176000000000000000000" , |
740 | "71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000" , |
741 | "5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000" , |
742 | "475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000" , |
743 | "39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000" , |
744 | "3314240134565353266999387579130131288000666286242049487118846032383059131291716864129885722968716753156177920000000000000000000" , |
745 | "281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000" , |
746 | "24227095383672732381765523203441259715284870552429381750838764496720162249742450276789464634901319465571660595200000000000000000000" , |
747 | "2107757298379527717213600518699389595229783738061356212322972511214654115727593174080683423236414793504734471782400000000000000000000" , |
748 | "185482642257398439114796845645546284380220968949399346684421580986889562184028199319100141244804501828416633516851200000000000000000000" , |
749 | "16507955160908461081216919262453619309839666236496541854913520707833171034378509739399912570787600662729080382999756800000000000000000000" , |
750 | "1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000" , |
751 | "135200152767840296255166568759495142147586866476906677791741734597153670771559994765685283954750449427751168336768008192000000000000000000000" , |
752 | "12438414054641307255475324325873553077577991715875414356840239582938137710983519518443046123837041347353107486982656753664000000000000000000000" , |
753 | "1156772507081641574759205162306240436214753229576413535186142281213246807121467315215203289516844845303838996289387078090752000000000000000000000" , |
754 | "108736615665674308027365285256786601004186803580182872307497374434045199869417927630229109214583415458560865651202385340530688000000000000000000000" , |
755 | "10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000" , |
756 | "991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000" , |
757 | "96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000" , |
758 | "9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000" , |
759 | "933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000" , |
760 | "93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000" , |
761 | }; |
762 | |
763 | static BOOST_MATH_THREAD_LOCAL T factorials[sizeof(factorial_strings) / sizeof(factorial_strings[0])]; |
764 | static BOOST_MATH_THREAD_LOCAL int digits = 0; |
765 | |
766 | int current_digits = boost::math::tools::digits<T>(); |
767 | |
768 | if(digits != current_digits) |
769 | { |
770 | digits = current_digits; |
771 | for(unsigned k = 0; k < sizeof(factorials) / sizeof(factorials[0]); ++k) |
772 | factorials[k] = static_cast<T>(boost::math::tools::convert_from_string<T>(factorial_strings[k])); |
773 | } |
774 | |
775 | return factorials[i]; |
776 | } |
777 | |
778 | template <class T> |
779 | inline T unchecked_factorial_imp(unsigned i, const boost::integral_constant<int, std::numeric_limits<float>::digits>&) |
780 | { |
781 | return unchecked_factorial<float>(i); |
782 | } |
783 | |
784 | template <class T> |
785 | inline T unchecked_factorial_imp(unsigned i, const boost::integral_constant<int, std::numeric_limits<double>::digits>&) |
786 | { |
787 | return unchecked_factorial<double>(i); |
788 | } |
789 | |
790 | #if DBL_MANT_DIG != LDBL_MANT_DIG |
791 | template <class T> |
792 | inline T unchecked_factorial_imp(unsigned i, const boost::integral_constant<int, LDBL_MANT_DIG>&) |
793 | { |
794 | return unchecked_factorial<long double>(i); |
795 | } |
796 | #endif |
797 | #ifdef BOOST_MATH_USE_FLOAT128 |
798 | template <class T> |
799 | inline T unchecked_factorial_imp(unsigned i, const boost::integral_constant<int, 113>&) |
800 | { |
801 | return unchecked_factorial<BOOST_MATH_FLOAT128_TYPE>(i); |
802 | } |
803 | #endif |
804 | |
805 | template <class T> |
806 | inline T unchecked_factorial(unsigned i) |
807 | { |
808 | typedef typename boost::math::policies::precision<T, boost::math::policies::policy<> >::type tag_type; |
809 | return unchecked_factorial_imp<T>(i, tag_type()); |
810 | } |
811 | |
812 | #ifdef BOOST_MATH_USE_FLOAT128 |
813 | #define BOOST_MATH_DETAIL_FLOAT128_MAX_FACTORIAL : std::numeric_limits<T>::digits == 113 ? max_factorial<BOOST_MATH_FLOAT128_TYPE>::value |
814 | #else |
815 | #define BOOST_MATH_DETAIL_FLOAT128_MAX_FACTORIAL |
816 | #endif |
817 | |
818 | template <class T> |
819 | struct max_factorial |
820 | { |
821 | BOOST_STATIC_CONSTANT(unsigned, value = |
822 | std::numeric_limits<T>::digits == std::numeric_limits<float>::digits ? max_factorial<float>::value |
823 | : std::numeric_limits<T>::digits == std::numeric_limits<double>::digits ? max_factorial<double>::value |
824 | : std::numeric_limits<T>::digits == std::numeric_limits<long double>::digits ? max_factorial<long double>::value |
825 | BOOST_MATH_DETAIL_FLOAT128_MAX_FACTORIAL |
826 | : 100); |
827 | }; |
828 | |
829 | #undef BOOST_MATH_DETAIL_FLOAT128_MAX_FACTORIAL |
830 | |
831 | #else // BOOST_MATH_NO_LEXICAL_CAST |
832 | |
833 | template <class T> |
834 | inline T unchecked_factorial(unsigned i BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T)) |
835 | { |
836 | return 1; |
837 | } |
838 | |
839 | template <class T> |
840 | struct max_factorial |
841 | { |
842 | BOOST_STATIC_CONSTANT(unsigned, value = 0); |
843 | }; |
844 | |
845 | #endif |
846 | |
847 | #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION |
848 | template <class T> |
849 | const unsigned max_factorial<T>::value; |
850 | #endif |
851 | |
852 | } // namespace math |
853 | } // namespace boost |
854 | |
855 | #endif // BOOST_MATH_SP_UC_FACTORIALS_HPP |
856 | |
857 | |