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1 | // (C) Copyright John Maddock 2006-8. |
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_BIG_LANCZOS_HPP | |
7 | #define BOOST_BIG_LANCZOS_HPP | |
8 | ||
9 | #include <boost/math/special_functions/lanczos.hpp> | |
10 | ||
11 | namespace boost{ namespace math{ namespace lanczos{ | |
12 | ||
13 | // | |
14 | // Lanczos Coefficients for N=13 G=13.144565 | |
15 | // Max experimental error (with arbitary precision arithmetic) 9.2213e-23 | |
16 | // Generated with compiler: Microsoft Visual C++ version 8.0 on Win32 at Mar 23 2006 | |
17 | // | |
18 | typedef lanczos13 lanczos13UDT; | |
19 | ||
20 | // | |
21 | // Lanczos Coefficients for N=22 G=22.61891 | |
22 | // Max experimental error (with arbitary precision arithmetic) 2.9524e-38 | |
23 | // Generated with compiler: Microsoft Visual C++ version 8.0 on Win32 at Mar 23 2006 | |
24 | // | |
25 | struct lanczos22UDT : public mpl::int_<120> | |
26 | { | |
27 | // | |
28 | // Produces slightly better than 128-bit long-double precision when | |
29 | // evaluated at higher precision: | |
30 | // | |
31 | template <class T> | |
32 | static T lanczos_sum(const T& z) | |
33 | { | |
34 | lanczos_initializer<lanczos22UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
35 | static const T num[22] = { | |
36 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 46198410803245094237463011094.12173081986)), | |
37 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 43735859291852324413622037436.321513777)), | |
38 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 19716607234435171720534556386.97481377748)), | |
39 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 5629401471315018442177955161.245623932129)), | |
40 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1142024910634417138386281569.245580222392)), | |
41 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 175048529315951173131586747.695329230778)), | |
42 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 21044290245653709191654675.41581372963167)), | |
43 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 2033001410561031998451380.335553678782601)), | |
44 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 160394318862140953773928.8736211601848891)), | |
45 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 10444944438396359705707.48957290388740896)), | |
46 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 565075825801617290121.1466393747967538948)), | |
47 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 25475874292116227538.99448534450411942597)), | |
48 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 957135055846602154.6720835535232270205725)), | |
49 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 29874506304047462.23662392445173880821515)), | |
50 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 769651310384737.2749087590725764959689181)), | |
51 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 16193289100889.15989633624378404096011797)), | |
52 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 273781151680.6807433264462376754578933261)), | |
53 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 3630485900.32917021712188739762161583295)), | |
54 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 36374352.05577334277856865691538582936484)), | |
55 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 258945.7742115532455441786924971194951043)), | |
56 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1167.501919472435718934219997431551246996)), | |
57 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 2.50662827463100050241576528481104525333)) | |
58 | }; | |
59 | static const T denom[22] = { | |
60 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.0)), | |
61 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 2432902008176640000.0)), | |
62 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 8752948036761600000.0)), | |
63 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 13803759753640704000.0)), | |
64 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 12870931245150988800.0)), | |
65 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 8037811822645051776.0)), | |
66 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 3599979517947607200.0)), | |
67 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1206647803780373360.0)), | |
68 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 311333643161390640.0)), | |
69 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 63030812099294896.0)), | |
70 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 10142299865511450.0)), | |
71 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1307535010540395.0)), | |
72 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 135585182899530.0)), | |
73 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 11310276995381.0)), | |
74 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 756111184500.0)), | |
75 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 40171771630.0)), | |
76 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1672280820.0)), | |
77 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 53327946.0)), | |
78 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1256850.0)), | |
79 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 20615.0)), | |
80 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 210.0)), | |
81 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1.0)) | |
82 | }; | |
83 | return boost::math::tools::evaluate_rational(num, denom, z); | |
84 | } | |
85 | ||
86 | template <class T> | |
87 | static T lanczos_sum_expG_scaled(const T& z) | |
88 | { | |
89 | lanczos_initializer<lanczos22UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
90 | static const T num[22] = { | |
91 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 6939996264376682180.277485395074954356211)), | |
92 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 6570067992110214451.87201438870245659384)), | |
93 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 2961859037444440551.986724631496417064121)), | |
94 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 845657339772791245.3541226499766163431651)), | |
95 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 171556737035449095.2475716923888737881837)), | |
96 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 26296059072490867.7822441885603400926007)), | |
97 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 3161305619652108.433798300149816829198706)), | |
98 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 305400596026022.4774396904484542582526472)), | |
99 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 24094681058862.55120507202622377623528108)), | |
100 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1569055604375.919477574824168939428328839)), | |
101 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 84886558909.02047889339710230696942513159)), | |
102 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 3827024985.166751989686050643579753162298)), | |
103 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 143782298.9273215199098728674282885500522)), | |
104 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 4487794.24541641841336786238909171265944)), | |
105 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 115618.2025760830513505888216285273541959)), | |
106 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 2432.580773108508276957461757328744780439)), | |
107 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 41.12782532742893597168530008461874360191)), | |
108 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.5453771709477689805460179187388702295792)), | |
109 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.005464211062612080347167337964166505282809)), | |
110 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.388992321263586767037090706042788910953e-4)), | |
111 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.1753839324538447655939518484052327068859e-6)), | |
112 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.3765495513732730583386223384116545391759e-9)) | |
113 | }; | |
114 | static const T denom[22] = { | |
115 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.0)), | |
116 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 2432902008176640000.0)), | |
117 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 8752948036761600000.0)), | |
118 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 13803759753640704000.0)), | |
119 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 12870931245150988800.0)), | |
120 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 8037811822645051776.0)), | |
121 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 3599979517947607200.0)), | |
122 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1206647803780373360.0)), | |
123 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 311333643161390640.0)), | |
124 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 63030812099294896.0)), | |
125 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 10142299865511450.0)), | |
126 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1307535010540395.0)), | |
127 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 135585182899530.0)), | |
128 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 11310276995381.0)), | |
129 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 756111184500.0)), | |
130 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 40171771630.0)), | |
131 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1672280820.0)), | |
132 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 53327946.0)), | |
133 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1256850.0)), | |
134 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 20615.0)), | |
135 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 210.0)), | |
136 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1.0)) | |
137 | }; | |
138 | return boost::math::tools::evaluate_rational(num, denom, z); | |
139 | } | |
140 | ||
141 | ||
142 | template<class T> | |
143 | static T lanczos_sum_near_1(const T& dz) | |
144 | { | |
145 | lanczos_initializer<lanczos22UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
146 | static const T d[21] = { | |
147 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 8.318998691953337183034781139546384476554)), | |
148 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -63.15415991415959158214140353299240638675)), | |
149 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 217.3108224383632868591462242669081540163)), | |
150 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -448.5134281386108366899784093610397354889)), | |
151 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 619.2903759363285456927248474593012711346)), | |
152 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -604.1630177420625418522025080080444177046)), | |
153 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 428.8166750424646119935047118287362193314)), | |
154 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -224.6988753721310913866347429589434550302)), | |
155 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 87.32181627555510833499451817622786940961)), | |
156 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -25.07866854821128965662498003029199058098)), | |
157 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 5.264398125689025351448861011657789005392)), | |
158 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.792518936256495243383586076579921559914)), | |
159 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.08317448364744713773350272460937904691566)), | |
160 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.005845345166274053157781068150827567998882)), | |
161 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.0002599412126352082483326238522490030412391)), | |
162 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.6748102079670763884917431338234783496303e-5)), | |
163 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.908824383434109002762325095643458603605e-7)), | |
164 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.5299325929309389890892469299969669579725e-9)), | |
165 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.994306085859549890267983602248532869362e-12)), | |
166 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.3499893692975262747371544905820891835298e-15)), | |
167 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.7260746353663365145454867069182884694961e-20)), | |
168 | }; | |
169 | T result = 0; | |
170 | for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k) | |
171 | { | |
172 | result += (-d[k-1]*dz)/(k*dz + k*k); | |
173 | } | |
174 | return result; | |
175 | } | |
176 | ||
177 | template<class T> | |
178 | static T lanczos_sum_near_2(const T& dz) | |
179 | { | |
180 | static const T d[21] = { | |
181 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 75.39272007105208086018421070699575462226)), | |
182 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -572.3481967049935412452681346759966390319)), | |
183 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1969.426202741555335078065370698955484358)), | |
184 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -4064.74968778032030891520063865996757519)), | |
185 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 5612.452614138013929794736248384309574814)), | |
186 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -5475.357667500026172903620177988213902339)), | |
187 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 3886.243614216111328329547926490398103492)), | |
188 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -2036.382026072125407192448069428134470564)), | |
189 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 791.3727954936062108045551843636692287652)), | |
190 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -227.2808432388436552794021219198885223122)), | |
191 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 47.70974355562144229897637024320739257284)), | |
192 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -7.182373807798293545187073539819697141572)), | |
193 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.7537866989631514559601547530490976100468)), | |
194 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.05297470142240154822658739758236594717787)), | |
195 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.00235577330936380542539812701472320434133)), | |
196 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.6115613067659273118098229498679502138802e-4)), | |
197 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.8236417010170941915758315020695551724181e-6)), | |
198 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.4802628430993048190311242611330072198089e-8)), | |
199 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.9011113376981524418952720279739624707342e-11)), | |
200 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.3171854152689711198382455703658589996796e-14)), | |
201 | static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.6580207998808093935798753964580596673177e-19)), | |
202 | }; | |
203 | T result = 0; | |
204 | T z = dz + 2; | |
205 | for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k) | |
206 | { | |
207 | result += (-d[k-1]*dz)/(z + k*z + k*k - 1); | |
208 | } | |
209 | return result; | |
210 | } | |
211 | ||
212 | static double g(){ return 22.61890999999999962710717227309942245483; } | |
213 | }; | |
214 | // | |
215 | // Lanczos Coefficients for N=31 G=32.08067 | |
216 | // Max experimental error (with arbitary precision arithmetic) 0.162e-52 | |
217 | // Generated with compiler: Microsoft Visual C++ version 8.0 on Win32 at May 9 2006 | |
218 | // | |
219 | struct lanczos31UDT | |
220 | { | |
221 | template <class T> | |
222 | static T lanczos_sum(const T& z) | |
223 | { | |
224 | lanczos_initializer<lanczos31UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
225 | static const T num[31] = { | |
226 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.2579646553333513328235723061836959833277e46)), | |
227 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.2444796504337453845497419271639377138264e46)), | |
228 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.1119885499016017172212179730662673475329e46)), | |
229 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.3301983829072723658949204487793889113715e45)), | |
230 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.7041171040503851585152895336505379417066e44)), | |
231 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.1156687509001223855125097826246939403504e44)), | |
232 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1522559363393940883866575697565974893306000)), | |
233 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 164914363507650839510801418717701057005700)), | |
234 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 14978522943127593263654178827041568394060)), | |
235 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1156707153701375383907746879648168666774)), | |
236 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 76739431129980851159755403434593664173.2)), | |
237 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4407916278928188620282281495575981079.306)), | |
238 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 220487883931812802092792125175269667.3004)), | |
239 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 9644828280794966468052381443992828.433924)), | |
240 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 369996467042247229310044531282837.6549068)), | |
241 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 12468380890717344610932904378961.13494291)), | |
242 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 369289245210898235894444657859.0529720075)), | |
243 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 9607992460262594951559461829.34885209022)), | |
244 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 219225935074853412540086410.981421315799)), | |
245 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4374309943598658046326340.720767382079549)), | |
246 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 76008779092264509404014.10530947173485581)), | |
247 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1143503533822162444712.335663112617754987)), | |
248 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 14779233719977576920.37884890049671578409)), | |
249 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 162409028440678302.9992838032166348069916)), | |
250 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1496561553388385.733407609544964535634135)), | |
251 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 11347624460661.81008311053190661436107043)), | |
252 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 68944915931.32004991941950530448472223832)), | |
253 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 322701221.6391432296123937035480931903651)), | |
254 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1092364.213992634267819050120261755371294)), | |
255 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2380.151399852411512711176940867823024864)), | |
256 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2.506628274631000502415765284811045253007)), | |
257 | }; | |
258 | static const T denom[31] = { | |
259 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0)), | |
260 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.8841761993739701954543616e31)), | |
261 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.3502799997985980526649278464e32)), | |
262 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.622621928420356134910574592e32)), | |
263 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 66951000306085302338993639424000)), | |
264 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 49361465831621147825759587123200)), | |
265 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 26751280755793398822580822142976)), | |
266 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 11139316913434780466101123891200)), | |
267 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 3674201658710345201899117607040)), | |
268 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 981347603630155088295475765440)), | |
269 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 215760462268683520394805979744)), | |
270 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 39539238727270799376544542000)), | |
271 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 6097272817323042122728617800)), | |
272 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 796974693974455191377937300)), | |
273 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 88776380550648116217781890)), | |
274 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 8459574446076318147830625)), | |
275 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 691254538651580660999025)), | |
276 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 48487623689430693038025)), | |
277 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2918939500751087661105)), | |
278 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 150566737512021319125)), | |
279 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 6634460278534540725)), | |
280 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 248526574856284725)), | |
281 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 7860403394108265)), | |
282 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 207912996295875)), | |
283 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4539323721075)), | |
284 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 80328850875)), | |
285 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1122686019)), | |
286 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 11921175)), | |
287 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 90335)), | |
288 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 435)), | |
289 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1)), | |
290 | }; | |
291 | return boost::math::tools::evaluate_rational(num, denom, z, 31); | |
292 | } | |
293 | ||
294 | template <class T> | |
295 | static T lanczos_sum_expG_scaled(const T& z) | |
296 | { | |
297 | lanczos_initializer<lanczos31UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
298 | static const T num[31] = { | |
299 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 30137154810677525966583148469478.52374216)), | |
300 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 28561746428637727032849890123131.36314653)), | |
301 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 13083250730789213354063781611435.74046294)), | |
302 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 3857598154697777600846539129354.783647)), | |
303 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 822596651552555685068015316144.0952185852)), | |
304 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 135131964033213842052904200372.039133532)), | |
305 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 17787555889683709693655685146.19771358863)), | |
306 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1926639793777927562221423874.149673297196)), | |
307 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 174989113988888477076973808.6991839697774)), | |
308 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 13513425905835560387095425.01158383184045)), | |
309 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 896521313378762433091075.1446749283094845)), | |
310 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 51496223433749515758124.71524415105430686)), | |
311 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2575886794780078381228.37205955912263407)), | |
312 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 112677328855422964200.4155776009524490958)), | |
313 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4322545967487943330.625233358130724324796)), | |
314 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 145663957202380774.0362027607207590519723)), | |
315 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4314283729473470.686566233465428332496534)), | |
316 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 112246988185485.8877916434026906290603878)), | |
317 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2561143864972.040563435178307062626388193)), | |
318 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 51103611767.9626550674442537989885239605)), | |
319 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 887985348.0369447209508500133077232094491)), | |
320 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 13359172.3954672607019822025834072685839)), | |
321 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 172660.8841147568768783928167105965064459)), | |
322 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1897.370795407433013556725714874693719617)), | |
323 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 17.48383210090980598861217644749573257178)), | |
324 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.1325705316732132940835251054350153028901)), | |
325 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.0008054605783673449641889260501816356090452)), | |
326 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.377001130700104515644336869896819162464e-5)), | |
327 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.1276172868883867038813825443204454996531e-7)), | |
328 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.2780651912081116274907381023821492811093e-10)), | |
329 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.2928410648650955854121639682890739211234e-13)), | |
330 | }; | |
331 | static const T denom[31] = { | |
332 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0)), | |
333 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.8841761993739701954543616e31)), | |
334 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.3502799997985980526649278464e32)), | |
335 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.622621928420356134910574592e32)), | |
336 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 66951000306085302338993639424000)), | |
337 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 49361465831621147825759587123200)), | |
338 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 26751280755793398822580822142976)), | |
339 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 11139316913434780466101123891200)), | |
340 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 3674201658710345201899117607040)), | |
341 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 981347603630155088295475765440)), | |
342 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 215760462268683520394805979744)), | |
343 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 39539238727270799376544542000)), | |
344 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 6097272817323042122728617800)), | |
345 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 796974693974455191377937300)), | |
346 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 88776380550648116217781890)), | |
347 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 8459574446076318147830625)), | |
348 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 691254538651580660999025)), | |
349 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 48487623689430693038025)), | |
350 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2918939500751087661105)), | |
351 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 150566737512021319125)), | |
352 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 6634460278534540725)), | |
353 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 248526574856284725)), | |
354 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 7860403394108265)), | |
355 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 207912996295875)), | |
356 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4539323721075)), | |
357 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 80328850875)), | |
358 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1122686019)), | |
359 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 11921175)), | |
360 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 90335)), | |
361 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 435)), | |
362 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1)), | |
363 | }; | |
364 | return boost::math::tools::evaluate_rational(num, denom, z, 31); | |
365 | } | |
366 | ||
367 | ||
368 | template<class T> | |
369 | static T lanczos_sum_near_1(const T& dz) | |
370 | { | |
371 | lanczos_initializer<lanczos31UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
372 | static const T d[30] = { | |
373 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 11.80038544942943603508206880307972596807)), | |
374 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -130.6355975335626214564236363322099481079)), | |
375 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 676.2177719145993049893392276809256538927)), | |
376 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -2174.724497783850503069990936574060452057)), | |
377 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4869.877180638131076410069103742986502022)), | |
378 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -8065.744271864238179992762265472478229172)), | |
379 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 10245.03825618572106228191509520638651539)), | |
380 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -10212.83902362683215459850403668669647192)), | |
381 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 8110.289185383288952562767679576754140336)), | |
382 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -5179.310892558291062401828964000776095156)), | |
383 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2673.987492589052370230989109591011091273)), | |
384 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1118.342574651205183051884250033505609141)), | |
385 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 378.5812742511620662650096436471920295596)), | |
386 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -103.3725999812126067084828735543906768961)), | |
387 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 22.62913974335996321848099677797888917792)), | |
388 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -3.936414819950859548507275533569588041446)), | |
389 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.5376818198843817355682124535902641644854)), | |
390 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.0567827903603478957483409124122554243201)), | |
391 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.004545544993648879420352693271088478106482)), | |
392 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.0002689795568951033950042375135970897959935)), | |
393 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.1139493459006846530734617710847103572122e-4)), | |
394 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.3316581197839213921885210451302820192794e-6)), | |
395 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.6285613334898374028443777562554713906213e-8)), | |
396 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.7222145115734409070310317999856424167091e-10)), | |
397 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.4562976983547274766890241815002584238219e-12)), | |
398 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.1380593023819058919640038942493212141072e-14)), | |
399 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.1629663871586410129307496385264268190679e-17)), | |
400 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.5429994291916548849493889660077076739993e-21)), | |
401 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.2922682842441892106795386303084661338957e-25)), | |
402 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.8456967065309046044689041041336866118459e-31)), | |
403 | }; | |
404 | T result = 0; | |
405 | for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k) | |
406 | { | |
407 | result += (-d[k-1]*dz)/(k*dz + k*k); | |
408 | } | |
409 | return result; | |
410 | } | |
411 | ||
412 | template<class T> | |
413 | static T lanczos_sum_near_2(const T& dz) | |
414 | { | |
415 | lanczos_initializer<lanczos31UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
416 | static const T d[30] = { | |
417 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 147.9979641587472136175636384176549713358)), | |
418 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1638.404318611773924210055619836375434296)), | |
419 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 8480.981744216135641122944743711911653273)), | |
420 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -27274.93942104458448200467097634494071176)), | |
421 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 61076.98019918759324489193232276937262854)), | |
422 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -101158.8762737154296509560513952101409264)), | |
423 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 128491.1252383947174824913796141607174379)), | |
424 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -128087.2892038336581928787480535905496026)), | |
425 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 101717.5492545853663296795562084430123258)), | |
426 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -64957.8330410311808907869707511362206858)), | |
427 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 33536.59139229792478811870738772305570317)), | |
428 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -14026.01847115365926835980820243003785821)), | |
429 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4748.087094096186515212209389240715050212)), | |
430 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1296.477510211815971152205100242259733245)), | |
431 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 283.8099337545793198947620951499958085157)), | |
432 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -49.36969067101255103452092297769364837753)), | |
433 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 6.743492833270653628580811118017061581404)), | |
434 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.7121578704864048548351804794951487823626)), | |
435 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.0570092738016915476694118877057948681298)), | |
436 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.003373485297696102660302960722607722438643)), | |
437 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.0001429128843527532859999752593761934089751)), | |
438 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.41595867130858508233493767243236888636e-5)), | |
439 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.7883284669307241040059778207492255409785e-7)), | |
440 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.905786322462384670803148223703187214379e-9)), | |
441 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.5722790216999820323272452464661250331451e-11)), | |
442 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.1731510870832349779315841757234562309727e-13)), | |
443 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.2043890314358438601429048378015983874378e-16)), | |
444 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.6810185176079344204740000170500311171065e-20)), | |
445 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.3665567641131713928114853776588342403919e-24)), | |
446 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.1060655106553177007425710511436497259484e-29)), | |
447 | }; | |
448 | T result = 0; | |
449 | T z = dz + 2; | |
450 | for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k) | |
451 | { | |
452 | result += (-d[k-1]*dz)/(z + k*z + k*k - 1); | |
453 | } | |
454 | return result; | |
455 | } | |
456 | ||
457 | static double g(){ return 32.08066999999999779902282170951366424561; } | |
458 | }; | |
459 | ||
460 | // | |
461 | // Lanczos Coefficients for N=61 G=63.192152 | |
462 | // Max experimental error (with 1000-bit precision arithmetic) 3.740e-113 | |
463 | // Generated with compiler: Microsoft Visual C++ version 8.0 on Win32 at Mar 12 2006 | |
464 | // | |
465 | struct lanczos61UDT | |
466 | { | |
467 | template <class T> | |
468 | static T lanczos_sum(const T& z) | |
469 | { | |
470 | lanczos_initializer<lanczos61UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
471 | using namespace boost; | |
472 | static const T d[61] = { | |
473 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2.50662827463100050241576528481104525300698674060993831662992357634229365460784197494659584)), | |
474 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 13349415823254323512107320481.3495396037261649201426994438803767191136434970492309775123879)), | |
475 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -300542621510568204264185787475.230003734889859348050696493467253861933279360152095861484548)), | |
476 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 3273919938390136737194044982676.40271056035622723775417608127544182097346526115858803376474)), | |
477 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -22989594065095806099337396006399.5874206181563663855129141706748733174902067950115092492439)), | |
478 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 116970582893952893160414263796102.542775878583510989850142808618916073286745084692189044738)), | |
479 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -459561969036479455224850813196807.283291532483532558959779434457349912822256480548436066098)), | |
480 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1450959909778264914956547227964788.89797179379520834974601372820249784303794436366366810477)), | |
481 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -3782846865486775046285288437885921.41537699732805465141128848354901016102326190612528503251)), | |
482 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 8305043213936355459145388670886540.09976337905520168067329932809302445437208115570138102767)), | |
483 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -15580988484396722546934484726970745.4927787160273626078250810989811865283255762028143642311)), | |
484 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 25262722284076250779006793435537600.0822901485517345545978818780090308947301031347345640449)), | |
485 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -35714428027687018805443603728757116.5304655170478705341887572982734901197345415291580897698)), | |
486 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 44334726194692443174715432419157343.2294160783772787096321009453791271387235388689346602833)), | |
487 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -48599573547617297831555162417695106.187829304963846482633791012658974681648157963911491985)), | |
488 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 47258466493366798944386359199482189.0753349196625125615316002614813737880755896979754845101)), | |
489 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -40913448215392412059728312039233342.142914753896559359297977982314043378636755884088383226)), | |
490 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 31626312914486892948769164616982902.7262756989418188077611392594232674722318027323102462687)), | |
491 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -21878079174441332123064991795834438.4699982361692990285700077902601657354101259411789722708)), | |
492 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 13567268503974326527361474986354265.3136632133935430378937191911532112778452274286122946396)), | |
493 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -7551494211746723529747611556474669.62996644923557605747803028485900789337467673523741066527)), | |
494 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 3775516572689476384052312341432597.70584966904950490541958869730702790312581801585742038997)), | |
495 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1696271471453637244930364711513292.79902955514107737992185368006225264329876265486853482449)), | |
496 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 684857608019352767999083000986166.20765273693720041519286231015176745354062413008561259139)), | |
497 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -248397566275708464679881624417990.410438107634139924805871051723444048539177890346227250473)), | |
498 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 80880368999557992138783568858556.1512378233079327986518410244522800950609595592170022878937)), | |
499 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -23618197945394013802495450485616.9025005749893350650829964098117490779655546610665927669729)), | |
500 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 6176884636893816103087134481332.06708966653493024119556843727320635285468825056891248447124)), | |
501 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1444348683723439589948246285262.64080678953468490544615312565485170860503207005915261691108)), | |
502 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 301342031656979076702313946827.961658905182634508217626783081241074250132289461989777865387)), | |
503 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -55959656587719766738301589651.3940625826610668990368881615587469329021742236397809951765678)), | |
504 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 9223339169004064297247180402.36227016155682738556103138196079389248843082157924368301293963)), | |
505 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1344882881571942601385730283.42710150182526891377514071881534880944872423492272147871101373)), | |
506 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 172841913316760599352601139.54409257740173055624405575900164401527761357324625574736896079)), | |
507 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -19496120443876233531343952.3802212016691702737346568192063937387825469602063310488794471653)), | |
508 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1920907372583710284097959.44121420322495784420169085871802458519363819782779653621724219067)), | |
509 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -164429314798240461613359.399597503536657962383155875723527581699785846599051112719962464604)), | |
510 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 12154026644351189572525.1452249886865981747374191977801688548318519692423556934568426042152)), | |
511 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -770443988366210815096.519382051977221101156336663806705367929328924137169970381042234329058)), | |
512 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 41558909851418707920.4696085656889424895313728719601503526476333404973280596225722152966128)), | |
513 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1890879946549708819.24562220042687554209318172044783707920086716716717574156283898330017796)), | |
514 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 71844996557297623.9583461685535340440524052492427928388171299145330229958643439878608673403)), | |
515 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -2253785109518255.55600197759875781765803818232939130127735487613049577235879610065545755637)), | |
516 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 57616883849355.997562563968344493719962252675875692642406455612671495250543228005045106721)), | |
517 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1182495730353.08218118278997948852215670614084013289033222774171548915344541249351599628436)), | |
518 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 19148649358.6196967288062261380599423925174178776792840639099120170800869284300966978300613)), | |
519 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -239779605.891370259668403359614360511661030470269478602533200704639655585967442891496784613)), | |
520 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2267583.00284368310957842936892685032434505866445291643236133553754152047677944820353796872)), | |
521 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -15749.490806784673108773558070497383604733010677027764233749920147549999361110299643477893)), | |
522 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 77.7059495149052727171505425584459982871343274332635726864135949842508025564999785370162956)), | |
523 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.261619987273930331397625130282851629108569607193781378836014468617185550622160348688297247)), | |
524 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.000572252321659691600529444769356185993188551770817110673186068921175991328434642504616377475)), | |
525 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.765167220661540041663007112207436426423746402583423562585653954743978584117929356523307954e-6)), | |
526 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.579179571056209077507916813937971472839851499147582627425979879366849876944438724610663401e-9)), | |
527 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.224804733043915149719206760378355636826808754704148660354494460792713189958510735070096991e-12)), | |
528 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.392711975389579343321746945135488409914483448652884894759297584020979857734289645857714768e-16)), | |
529 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.258603588346412049542768766878162221817684639789901440429511261589010049357907537684380983e-20)), | |
530 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.499992460848751668441190360024540741752242879565548017176883304716370989218399797418478685e-25)), | |
531 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.196211614533318174187346267877390498735734213905206562766348625767919122511096089367364025e-30)), | |
532 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.874722648949676363732094858062907290148733370978226751462386623191111439121706262759209573e-37)), | |
533 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.163907874717737848669759890242660846846105433791283903651924563157080252845636658802930428e-44)), | |
534 | }; | |
535 | T result = d[0]; | |
536 | for(unsigned k = 1; k < sizeof(d)/sizeof(d[0]); ++k) | |
537 | { | |
538 | result += d[k]/(z+(k-1)); | |
539 | } | |
540 | return result; | |
541 | } | |
542 | ||
543 | template <class T> | |
544 | static T lanczos_sum_expG_scaled(const T& z) | |
545 | { | |
546 | lanczos_initializer<lanczos61UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
547 | using namespace boost; | |
548 | static const T d[61] = { | |
549 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.901751806425638853077358552989167785490911341809902155556127108480303870921448984935411583e-27)), | |
550 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4.80241125306810017699523302110401965428995345115391817406006361151407344955277298373661032)), | |
551 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -108.119283021710869401330097315436214587270846871451487282117128515476478251641970487922552)), | |
552 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1177.78262074811362219818923738088833932279000985161077740440010901595132448469513438139561)), | |
553 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -8270.43570321334374279057432173814835581983913167617217749736484999327758232081395983082867)), | |
554 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 42079.807161997077661752306902088979258826568702655699995911391774839958572703348502730394)), | |
555 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -165326.003834443330215001219988296482004968548294447320869281647211603153902436231468280089)), | |
556 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 521978.361504895300685499370463597042533432134369277742485307843747923127933979566742421213)), | |
557 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1360867.51629992863544553419296636395576666570468519805449755596254912681418267100657262281)), | |
558 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2987713.73338656161102517003716335104823650191612448011720936412226357385029800040631754755)), | |
559 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -5605212.64915921452169919008770165304171481697939254152852673009005154549681704553438450709)), | |
560 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 9088186.58332916818449459635132673652700922052988327069535513580836143146727832380184335474)), | |
561 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -12848155.5543636394746355365819800465364996596310467415907815393346205151090486190421959769)), | |
562 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 15949281.2867656960575878805158849857756293807220033618942867694361569866468996967761600898)), | |
563 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -17483546.9948295433308250581770557182576171673272450149400973735206019559576269174369907171)), | |
564 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 17001087.8599749419660906448951424280111036786456594738278573653160553115681287326064596964)), | |
565 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -14718487.0643665950346574802384331125115747311674609017568623694516187494204567579595827859)), | |
566 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 11377468.7255609717716845971105161298889777425898291183866813269222281486121330837791392732)), | |
567 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -7870571.64253038587947746661946939286858490057774448573157856145556080330153403858747655263)), | |
568 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4880783.08440908743641723492059912671377140680710345996273343885045364205895751515063844239)), | |
569 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -2716626.7992639625103140035635916455652302249897918893040695025407382316653674141983775542)), | |
570 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1358230.46602865696544327299659410214201327791319846880787515156343361311278133805428800255)), | |
571 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -610228.440751458395860905749312275043435828322076830117123636938979942213530882048883969802)), | |
572 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 246375.416501158654327780901087115642493055617468601787093268312234390446439555559050129729)), | |
573 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -89360.2599028475206119333931211015869139511677735549267100272095432140508089207221096740632)), | |
574 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 29096.4637987498328341260960356772198979319790332957125131055960448759586930781530063775634)), | |
575 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -8496.57401431514433694413130585404918350686834939156759654375188338156288564260152505382438)), | |
576 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2222.11523574301594407443285016240908726891841242444092960094015874546135316534057865883047)), | |
577 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -519.599993280949289705514822058693289933461756514489674453254304308040888101533569480646682)), | |
578 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 108.406868361306987817730701109400305482972790224573776407166683184990131682003417239181112)), | |
579 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -20.1313142142558596796857948064047373605439974799116521459977609253211918146595346493447238)), | |
580 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 3.31806787671783168020012913552384112429614503798293169239082032849759155847394955909684383)), | |
581 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.483817477111537877685595212919784447924875428848331771524426361483392903320495411973587861)), | |
582 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.0621793463102927384924303843912913542297042029136293808338022462765755471002366206711862637)), | |
583 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.00701366932085103924241526535768453911099671087892444015581511551813219720807206445462785293)), | |
584 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.000691040514756294308758606917671220770856269030526647010461217455799229645004351524024364997)), | |
585 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.591529398871361458428147660822525365922497109038495896497692806150033516658042357799869656e-4)), | |
586 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.437237367535177689875119370170434437030440227275583289093139147244747901678407875809020739e-5)), | |
587 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.277164853397051135996651958345647824709602266382721185838782221179129726200661453504250697e-6)), | |
588 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.149506899012035980148891401548317536032574502641368034781671941165064546410613201579653674e-7)), | |
589 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.68023824066463262779882895193964639544061678698791279217407325790147925675797085217462974e-9)), | |
590 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.258460163734186329938721529982859244969655253624066115559707985878606277800329299821882688e-10)), | |
591 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.810792256024669306744649981276512583535251727474303382740940985102669076169168931092026491e-12)), | |
592 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.207274966207031327521921078048021807442500113231320959236850963529304158700096495799022922e-13)), | |
593 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.425399199286327802950259994834798737777721414442095221716122926637623478450472871269742436e-15)), | |
594 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.688866766744198529064607574117697940084548375790020728788313274612845280173338912495478431e-17)), | |
595 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.862599751805643281578607291655858333628582704771553874199104377131082877406179933909898885e-19)), | |
596 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.815756005678735657200275584442908437977926312650210429668619446123450972547018343768177988e-21)), | |
597 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.566583084099007858124915716926967268295318152203932871370429534546567151650626184750291695e-23)), | |
598 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.279544761599725082805446124351997692260093135930731230328454667675190245860598623539891708e-25)), | |
599 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.941169851584987983984201821679114408126982142904386301937192011680047611188837432096199601e-28)), | |
600 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.205866011331040736302780507155525142187875191518455173304638008169488993406425201915370746e-30)), | |
601 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.27526655245712584371295491216289353976964567057707464008951584303679019796521332324352501e-33)), | |
602 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.208358067979444305082929004102609366169534624348056112144990933897581971394396210379638792e-36)), | |
603 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.808728107661779323263133007119729988596844663194254976820030366188579170595441991680169012e-40)), | |
604 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.141276924383478964519776436955079978012672985961918248012931336621229652792338950573694356e-43)), | |
605 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.930318449287651389310440021745842417218125582685428432576258687100661462527604238849332053e-48)), | |
606 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.179870748819321661641184169834635133045197146966203370650788171790610563029431722308057539e-52)), | |
607 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.705865243912790337263229413370018392321238639017433365017168104310561824133229343750737083e-58)), | |
608 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.3146787805734405996448268100558028857930560442377698646099945108125281507396722995748398e-64)), | |
609 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.589653534231618730406843260601322236697428143603814281282790370329151249078338470962782338e-72)), | |
610 | }; | |
611 | T result = d[0]; | |
612 | for(unsigned k = 1; k < sizeof(d)/sizeof(d[0]); ++k) | |
613 | { | |
614 | result += d[k]/(z+(k-1)); | |
615 | } | |
616 | return result; | |
617 | } | |
618 | ||
619 | template<class T> | |
620 | static T lanczos_sum_near_1(const T& dz) | |
621 | { | |
622 | lanczos_initializer<lanczos61UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
623 | using namespace boost; | |
624 | static const T d[60] = { | |
625 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 23.2463658527729692390378860713647146932236940604550445351214987229819352880524561852919518)), | |
626 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -523.358012551815715084547614110229469295755088686612838322817729744722233637819564673967396)), | |
627 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 5701.12892340421080714956066268650092612647620400476183901625272640935853188559347587495571)), | |
628 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -40033.5506451901904954336453419007623117537868026994808919201793803506999271787018654246699)), | |
629 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 203689.884259074923009439144410340256983393397995558814367995938668111650624499963153485034)), | |
630 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -800270.648969745331278757692597096167418585957703057412758177038340791380011708874081291202)), | |
631 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 2526668.23380061659863999395867315313385499515711742092815402701950519696944982260718031476)), | |
632 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -6587362.57559198722630391278043503867973853468105110382293763174847657538179665571836023631)), | |
633 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 14462211.3454541602975917764900442754186801975533106565506542322063393991552960595701762805)), | |
634 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -27132375.1879227404375395522940895789625516798992585980380939378508607160857820002128106898)), | |
635 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 43991923.8735251977856804364757478459275087361742168436524951824945035673768875988985478116)), | |
636 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -62192284.0030124679010201921841372967696262036115679150017649233887633598058364494608060812)), | |
637 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 77203473.0770033513405070667417251568915937590689150831268228886281254637715669678358204991)), | |
638 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -84630180.2217173903516348977915150565994784278120192219937728967986198118628659866582594874)), | |
639 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 82294807.2253549409847505891112074804416229757832871133388349982640444405470371147991706317)), | |
640 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -71245738.2484649177928765605893043553453557808557887270209768163561363857395639001251515788)), | |
641 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 55073334.3180266913441333534260714059077572215147571872597651029894142803987981342430068594)), | |
642 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -38097984.1648990787690036742690550656061009857688125101191167768314179751258568264424911474)), | |
643 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 23625729.5032184580395130592017474282828236643586203914515183078852982915252442161768527976)), | |
644 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -13149998.4348054726172055622442157883429575511528431835657668083088902165366619827169829685)), | |
645 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 6574597.77221556423683199818131482663205682902023554728024972161230111356285973623550338976)), | |
646 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -2953848.1483469149918109110050192571921018042012905892107136410603990336401921230407043408)), | |
647 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1192595.29584357246380113611351829515963605337523874715861849584306265512819543347806085356)), | |
648 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -432553.812019608638388918135375154289816441900572658692369491476137741687213006403648722272)), | |
649 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 140843.215385933866391177743292449477205328233960902455943995092958295858485718885800427129)), | |
650 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -41128.186992679630058614841985110676526199977321524879849001760603476646382839182691529968)), | |
651 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 10756.2849191854701631989789887757784944313743544315113894758328432005767448056040879337769)), | |
652 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -2515.15559672041299884426826962296210458052543246529646213159169885444118227871246315458787)), | |
653 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 524.750087004805200600237632074908875763734578390662349666321453103782638818305404274166951)), | |
654 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -97.4468596421732493988298219295878130651986131393383646674144877163795143930682205035917965)), | |
655 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 16.0613108128210806736384551896802799172445298357754547684100294231532127326987175444453058)), | |
656 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -2.34194813526540240672426202485306862230641838409943369059203455578340880900483887447559874)), | |
657 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.300982934748016059399829007219431333744032924923669397318820178988611410275964499475465815)), | |
658 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.033950095985367909789000959795708551814461844488183964432565731809399824963680858993718525)), | |
659 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.00334502394288921146242772614150438404658527112198421937945605441697314216921393987758378122)), | |
660 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.000286333429067523984607730553301991502191011265745476190940771685897687956262049750683013485)), | |
661 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.211647426149364947402896718485536530479491688838087899435991994237067890628274492042231115e-4)), | |
662 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.134163345121302758109675190598169832775248626443483098532368562186356128620805552609175683e-5)), | |
663 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.723697303042715085329782938306424498336642078597508935450663080894255773653328980495047891e-7)), | |
664 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.329273487343139063533251321553223583999676337945788660475231347828772272134656322947906888e-8)), | |
665 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.12510922551028971731767784013117088894558604838820475961392154031378891971216135267744134e-9)), | |
666 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.392468958215589939603666430583400537413757786057185505426804034745840192914621891690369903e-11)), | |
667 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.100332717101049934370760667782927946803279422001380028508200697081188326364078428184546051e-12)), | |
668 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.205917088291197705194762747639836655808855850989058813560983717575008725393428497910009756e-14)), | |
669 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.333450178247893143608439314203175490705783992567107481617660357577257627854979230819461489e-16)), | |
670 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.417546693906616047110563550428133589051498362676394888715581845170969319500638944065594319e-18)), | |
671 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.394871691642184410859178529844325390739857256666676534513661579365702353214518478078730801e-20)), | |
672 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.274258012587811199757875927548699264063511843669070634471054184977334027224611843434000922e-22)), | |
673 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.135315354265459854889496635967343027244391821142592599244505313738163473730636430399785048e-24)), | |
674 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.455579032003288910408487905303223613382276173706542364543918076752861628464036586507967767e-27)), | |
675 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.99650703862462739161520123768147312466695159780582506041370833824093136783202694548427718e-30)), | |
676 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.1332444609228706921659395801935919548447859029572115502899861345555006827214220195650058e-32)), | |
677 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.100856999148765307000182397631280249632761913433008379786888200467467364474581430670889392e-35)), | |
678 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.39146979455613683472384690509165395074425354524713697428673406058157887065953366609738731e-39)), | |
679 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.683859606707931248105140296850112494069265272540298100341919970496564103098283709868586478e-43)), | |
680 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.450326344248604222735147147805963966503893913752040066400766411031387063854141246972061792e-47)), | |
681 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.870675378039492904184581895322153006461319724931909799151743284769901586333730037761678891e-52)), | |
682 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.341678395249272265744518787745356400350877656459401143889000625280131819505857966769964401e-57)), | |
683 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.152322191370871666358069530949353871960316638394428595988162174042653299702098929238880862e-63)), | |
684 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.285425405297633795767452984791738825078111150078605004958179057245980222485147999495352632e-71)), | |
685 | }; | |
686 | T result = 0; | |
687 | for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k) | |
688 | { | |
689 | result += (-d[k-1]*dz)/(k*dz + k*k); | |
690 | } | |
691 | return result; | |
692 | } | |
693 | ||
694 | template<class T> | |
695 | static T lanczos_sum_near_2(const T& dz) | |
696 | { | |
697 | lanczos_initializer<lanczos61UDT, T>::force_instantiate(); // Ensure our constants get initialized before main() | |
698 | using namespace boost; | |
699 | static const T d[60] = { | |
700 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 557.56438192770795764344217888434355281097193198928944200046501607026919782564033547346298)), | |
701 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -12552.748616427645475141433405567201788681683808077269330800392600825597799119572762385222)), | |
702 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 136741.650054039199076788077149441364242294724343897779563222338447737802381279007988884806)), | |
703 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -960205.223613240309942047656967301131022760634321049075674684679438471862998829007639437133)), | |
704 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 4885504.47588736223774859617054275229642041717942140469884121916073195308537421162982679289)), | |
705 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -19194501.738192166918904824982935279260356575935661514109550613809352009246483412530545583)), | |
706 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 60602169.8633537742937457094837494059849674261357199218329545854990149896822944801504450843)), | |
707 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -157997975.522506767297528502540724511908584668874487506510120462561270100749019845014382885)), | |
708 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 346876323.86092543685419723290495817330608574729543216092477261152247521712190505658568876)), | |
709 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -650770365.471136883718747607976242475416651908858429752332176373467422603953536408709972919)), | |
710 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1055146856.05909309330903130910708372830487315684258450293308627289334336871273080305128138)), | |
711 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1491682726.25614447429071368736790697283307005456720192465860871846879804207692411263924608)), | |
712 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1851726287.94866167094858600116562210167031458934987154557042242638980748286188183300900268)), | |
713 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -2029855953.68334371445800569238095379629407314338521720558391277508374519526853827142679839)), | |
714 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1973842002.53354868177824629525448788555435194808657489238517523691040148611221295436287925)), | |
715 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -1708829941.98209573247426625323314413060108441455314880934710595647408841619484540679859098)), | |
716 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 1320934627.12433688699625456833930317624783222321555050330381730035733198249283009357314954)), | |
717 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -913780636.858542526294419197161614811332299249415125108737474024007693329922089123296358727)), | |
718 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 566663423.929632170286007468016419798879660054391183200464733820209439185545886930103546787)), | |
719 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -315402880.436816230388857961460509181823167373029384218959199936902955049832392362044305869)), | |
720 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 157691811.550465734461741500275930418786875005567018699867961482249002625886064187146134966)), | |
721 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -70848085.5705405970640618473551954585013808128304384354476488268600720054598122945113512731)), | |
722 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 28604413.4050137708444142264980840059788755325900041515286382001704951527733220637586013815)), | |
723 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -10374808.7067303054787164054055989420809074792801592763124972441820101840292558840131568633)), | |
724 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 3378126.32016207486657791623723515804931231041318964254116390764473281291389374196880720069)), | |
725 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -986460.090390653140964189383080344920103075349535669020623874668558777188889544398718979744)), | |
726 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 257989.631187387317948158483575125380011593209850756066176921901006833159795100137743395985)), | |
727 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -60326.0391159227288325790327830741260824763549807922845004854215660451399733578621565837087)), | |
728 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 12586.1375399649496159880821645216260841794563919652590583420570326276086323953958907053394)), | |
729 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -2337.26417330316922535871922886167444795452055677161063205953141105726549966801856628447293)), | |
730 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 385.230745012608736644117458716226876976056390433401632749144285378123105481506733917763829)), | |
731 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -56.1716559403731491675970177460841997333796694857076749852739159067307309470690838101179615)), | |
732 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 7.21907953468550196348585224042498727840087634483369357697580053424523903859773769748599575)), | |
733 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.814293485887386870805786409956942772883474224091975496298369877683530509729332902182019049)), | |
734 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.0802304419995150047616460464220884371214157889148846405799324851793571580868840034085001373)), | |
735 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.00686771095380619535195996193943858680694970000948742557733102777115482017857981277171196115)), | |
736 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.000507636621977556438232617777542864427109623356049335590894564220687567763620803789858345916)), | |
737 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.32179095465362720747836116655088181481893063531138957363431280817392443948706754917605911e-4)), | |
738 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.173578890579848508947329833426585354230744194615295570820295052665075101971588563893718407e-5)), | |
739 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.789762880006288893888161070734302768702358633525134582027140158619195373770299678322596835e-7)), | |
740 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.300074637200885066788470310738617992259402710843493097610337134266720909870967550606601658e-8)), | |
741 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.941337297619721713151110244242536308266701344868601679868536153775533330272973088246835359e-10)), | |
742 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.24064815013182536657310186836079333949814111498828401548170442715552017773994482539471456e-11)), | |
743 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.493892399304811910466345686492277504628763169549384435563232052965821874553923373100791477e-13)), | |
744 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.799780678476644196901221989475355609743387528732994566453160178199295104357319723742820593e-15)), | |
745 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.100148627870893347527249092785257443532967736956154251497569191947184705954310833302770086e-16)), | |
746 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.947100256812658897084619699699028861352615460106539259289295071616221848196411749449858071e-19)), | |
747 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.657808193528898116367845405906343884364280888644748907819280236995018351085371701094007759e-21)), | |
748 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.324554050057463845012469010247790763753999056976705084126950591088538742509983426730851614e-23)), | |
749 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.10927068902162908990029309141242256163212535730975970310918370355165185052827948996110107e-25)), | |
750 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.239012340507870646690121104637467232366271566488184795459093215303237974655782634371712486e-28)), | |
751 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.31958700972990573259359660326375143524864710953063781494908314884519046349402409667329667e-31)), | |
752 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.241905641292988284384362036555782113275737930713192053073501265726048089991747342247551645e-34)), | |
753 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.93894080230619233745797029179332447129464915420290457418429337322820997038069119047864035e-38)), | |
754 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.164023814025085488413251990798690797467351995518990067783355251949198292596815470576539877e-41)), | |
755 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.108010831192689925518484618970761942019888832176355541674171850211917230280206410356465451e-45)), | |
756 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.208831600642796805563854019033577205240227465154130766898180386564934443551840379116390645e-50)), | |
757 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.819516067465171848863933747691434138146789031214932473898084756489529673230665363014007306e-56)), | |
758 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, 0.365344970579318347488211604761724311582675708113250505307342682118101409913523622073678179e-62)), | |
759 | static_cast<T>(BOOST_MATH_HUGE_CONSTANT(T, 150, -0.684593199208628857931267904308244537968349564351534581234005234847904343404822808648361291e-70)), | |
760 | }; | |
761 | T result = 0; | |
762 | T z = dz + 2; | |
763 | for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k) | |
764 | { | |
765 | result += (-d[k-1]*dz)/(z + k*z + k*k - 1); | |
766 | } | |
767 | return result; | |
768 | } | |
769 | ||
770 | static double g(){ return 63.19215200000000010049916454590857028961181640625; } | |
771 | }; | |
772 | ||
773 | }}} // namespaces | |
774 | ||
775 | #endif | |
776 | ||
777 |