a68g-math.h
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1 //! @file a68g-math.h
2 //! @author J. Marcel van der Veer
3 //!
4 //! @section Copyright
5 //!
6 //! This file is part of Algol68G - an Algol 68 compiler-interpreter.
7 //! Copyright 2001-2023 J. Marcel van der Veer .
8 //!
9 //! @section License
10 //!
11 //! This program is free software; you can redistribute it and/or modify it
12 //! under the terms of the GNU General Public License as published by the
13 //! Free Software Foundation; either version 3 of the License, or
14 //! (at your option) any later version.
15 //!
16 //! This program is distributed in the hope that it will be useful, but
17 //! WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
18 //! or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
19 //! more details. You should have received a copy of the GNU General Public
20 //! License along with this program. If not, see .
21
22 static const REAL_T factable[A68_MAX_FAC + 1] = {
23 /* 0 */ 1.000000000000000000000e0,
24 /* 1 */ 1.000000000000000000000e0,
25 /* 2 */ 2.000000000000000000000e0,
26 /* 3 */ 6.000000000000000000000e0,
27 /* 4 */ 2.400000000000000000000e1,
28 /* 5 */ 1.200000000000000000000e2,
29 /* 6 */ 7.200000000000000000000e2,
30 /* 7 */ 5.040000000000000000000e3,
31 /* 8 */ 4.032000000000000000000e4,
32 /* 9 */ 3.628800000000000000000e5,
33 /* 10 */ 3.628800000000000000000e6,
34 /* 11 */ 3.991680000000000000000e7,
35 /* 12 */ 4.790016000000000000000e8,
36 /* 13 */ 6.227020800000000000000e9,
37 /* 14 */ 8.717829120000000000000e10,
38 /* 15 */ 1.307674368000000000000e12,
39 /* 16 */ 2.092278988800000000000e13,
40 /* 17 */ 3.556874280960000000000e14,
41 /* 18 */ 6.402373705728000000000e15,
42 /* 19 */ 1.216451004088320000000e17,
43 /* 20 */ 2.432902008176640000000e18,
44 /* 21 */ 5.109094217170944000000e19,
45 /* 22 */ 1.124000727777607680000e21,
46 /* 23 */ 2.585201673888497664000e22,
47 /* 24 */ 6.204484017332394393600e23,
48 /* 25 */ 1.551121004333098598400e25,
49 /* 26 */ 4.032914611266056355840e26,
50 /* 27 */ 1.088886945041835216077e28,
51 /* 28 */ 3.048883446117138605015e29,
52 /* 29 */ 8.841761993739701954544e30,
53 /* 30 */ 2.652528598121910586363e32,
54 /* 31 */ 8.222838654177922817726e33,
55 /* 32 */ 2.631308369336935301672e35,
56 /* 33 */ 8.683317618811886495518e36,
57 /* 34 */ 2.952327990396041408476e38,
58 /* 35 */ 1.033314796638614492967e40,
59 /* 36 */ 3.719933267899012174680e41,
60 /* 37 */ 1.376375309122634504632e43,
61 /* 38 */ 5.230226174666011117600e44,
62 /* 39 */ 2.039788208119744335864e46,
63 /* 40 */ 8.159152832478977343456e47,
64 /* 41 */ 3.345252661316380710817e49,
65 /* 42 */ 1.405006117752879898543e51,
66 /* 43 */ 6.041526306337383563736e52,
67 /* 44 */ 2.658271574788448768044e54,
68 /* 45 */ 1.196222208654801945620e56,
69 /* 46 */ 5.502622159812088949850e57,
70 /* 47 */ 2.586232415111681806430e59,
71 /* 48 */ 1.241391559253607267086e61,
72 /* 49 */ 6.082818640342675608723e62,
73 /* 50 */ 3.041409320171337804361e64,
74 /* 51 */ 1.551118753287382280224e66,
75 /* 52 */ 8.065817517094387857166e67,
76 /* 53 */ 4.274883284060025564298e69,
77 /* 54 */ 2.308436973392413804721e71,
78 /* 55 */ 1.269640335365827592597e73,
79 /* 56 */ 7.109985878048634518540e74,
80 /* 57 */ 4.052691950487721675568e76,
81 /* 58 */ 2.350561331282878571829e78,
82 /* 59 */ 1.386831185456898357379e80,
83 /* 60 */ 8.320987112741390144276e81,
84 /* 61 */ 5.075802138772247988009e83,
85 /* 62 */ 3.146997326038793752565e85,
86 /* 63 */ 1.982608315404440064116e87,
87 /* 64 */ 1.268869321858841641034e89,
88 /* 65 */ 8.247650592082470666723e90,
89 /* 66 */ 5.443449390774430640037e92,
90 /* 67 */ 3.647111091818868528825e94,
91 /* 68 */ 2.480035542436830599601e96,
92 /* 69 */ 1.711224524281413113725e98,
93 /* 70 */ 1.197857166996989179607e100,
94 /* 71 */ 8.504785885678623175212e101,
95 /* 72 */ 6.123445837688608686152e103,
96 /* 73 */ 4.470115461512684340891e105,
97 /* 74 */ 3.307885441519386412260e107,
98 /* 75 */ 2.480914081139539809195e109,
99 /* 76 */ 1.885494701666050254988e111,
100 /* 77 */ 1.451830920282858696341e113,
101 /* 78 */ 1.132428117820629783146e115,
102 /* 79 */ 8.946182130782975286851e116,
103 /* 80 */ 7.156945704626380229481e118,
104 /* 81 */ 5.797126020747367985880e120,
105 /* 82 */ 4.753643337012841748421e122,
106 /* 83 */ 3.945523969720658651190e124,
107 /* 84 */ 3.314240134565353266999e126,
108 /* 85 */ 2.817104114380550276949e128,
109 /* 86 */ 2.422709538367273238177e130,
110 /* 87 */ 2.107757298379527717214e132,
111 /* 88 */ 1.854826422573984391148e134,
112 /* 89 */ 1.650795516090846108122e136,
113 /* 90 */ 1.485715964481761497310e138,
114 /* 91 */ 1.352001527678402962552e140,
115 /* 92 */ 1.243841405464130725548e142,
116 /* 93 */ 1.156772507081641574759e144,
117 /* 94 */ 1.087366156656743080274e146,
118 /* 95 */ 1.032997848823905926260e148,
119 /* 96 */ 9.916779348709496892096e149,
120 /* 97 */ 9.619275968248211985333e151,
121 /* 98 */ 9.426890448883247745626e153,
122 /* 99 */ 9.332621544394415268170e155,
123 /* 100 */ 9.332621544394415268170e157,
124 /* 101 */ 9.425947759838359420852e159,
125 /* 102 */ 9.614466715035126609269e161,
126 /* 103 */ 9.902900716486180407547e163,
127 /* 104 */ 1.029901674514562762385e166,
128 /* 105 */ 1.081396758240290900504e168,
129 /* 106 */ 1.146280563734708354534e170,
130 /* 107 */ 1.226520203196137939352e172,
131 /* 108 */ 1.324641819451828974500e174,
132 /* 109 */ 1.443859583202493582205e176,
133 /* 110 */ 1.588245541522742940425e178,
134 /* 111 */ 1.762952551090244663872e180,
135 /* 112 */ 1.974506857221074023537e182,
136 /* 113 */ 2.231192748659813646597e184,
137 /* 114 */ 2.543559733472187557120e186,
138 /* 115 */ 2.925093693493015690688e188,
139 /* 116 */ 3.393108684451898201198e190,
140 /* 117 */ 3.969937160808720895402e192,
141 /* 118 */ 4.684525849754290656574e194,
142 /* 119 */ 5.574585761207605881323e196,
143 /* 120 */ 6.689502913449127057588e198,
144 /* 121 */ 8.094298525273443739682e200,
145 /* 122 */ 9.875044200833601362412e202,
146 /* 123 */ 1.214630436702532967577e205,
147 /* 124 */ 1.506141741511140879795e207,
148 /* 125 */ 1.882677176888926099744e209,
149 /* 126 */ 2.372173242880046885677e211,
150 /* 127 */ 3.012660018457659544810e213,
151 /* 128 */ 3.856204823625804217357e215,
152 /* 129 */ 4.974504222477287440390e217,
153 /* 130 */ 6.466855489220473672507e219,
154 /* 131 */ 8.471580690878820510985e221,
155 /* 132 */ 1.118248651196004307450e224,
156 /* 133 */ 1.487270706090685728908e226,
157 /* 134 */ 1.992942746161518876737e228,
158 /* 135 */ 2.690472707318050483595e230,
159 /* 136 */ 3.659042881952548657690e232,
160 /* 137 */ 5.012888748274991661035e234,
161 /* 138 */ 6.917786472619488492228e236,
162 /* 139 */ 9.615723196941089004197e238,
163 /* 140 */ 1.346201247571752460588e241,
164 /* 141 */ 1.898143759076170969429e243,
165 /* 142 */ 2.695364137888162776589e245,
166 /* 143 */ 3.854370717180072770522e247,
167 /* 144 */ 5.550293832739304789551e249,
168 /* 145 */ 8.047926057471991944849e251,
169 /* 146 */ 1.174997204390910823948e254,
170 /* 147 */ 1.727245890454638911203e256,
171 /* 148 */ 2.556323917872865588581e258,
172 /* 149 */ 3.808922637630569726986e260,
173 /* 150 */ 5.713383956445854590479e262,
174 /* 151 */ 8.627209774233240431623e264,
175 /* 152 */ 1.311335885683452545607e267,
176 /* 153 */ 2.006343905095682394778e269,
177 /* 154 */ 3.089769613847350887959e271,
178 /* 155 */ 4.789142901463393876336e273,
179 /* 156 */ 7.471062926282894447084e275,
180 /* 157 */ 1.172956879426414428192e278,
181 /* 158 */ 1.853271869493734796544e280,
182 /* 159 */ 2.946702272495038326504e282,
183 /* 160 */ 4.714723635992061322407e284,
184 /* 161 */ 7.590705053947218729075e286,
185 /* 162 */ 1.229694218739449434110e289,
186 /* 163 */ 2.004401576545302577600e291,
187 /* 164 */ 3.287218585534296227263e293,
188 /* 165 */ 5.423910666131588774984e295,
189 /* 166 */ 9.003691705778437366474e297,
190 /* 167 */ 1.503616514864999040201e300,
191 /* 168 */ 2.526075744973198387538e302,
192 /* 169 */ 4.269068009004705274939e304,
193 /* 170 */ 7.257415615307998967397e306
194 };
195
196 static const REAL_T ln_factable[A68_MAX_FAC + 1] = {
197 /* 0 */ 0.000000000000000000000e0,
198 /* 1 */ 0.000000000000000000000e0,
199 /* 2 */ 6.931471805599453094172e-1,
200 /* 3 */ 1.791759469228055000812e0,
201 /* 4 */ 3.178053830347945619647e0,
202 /* 5 */ 4.787491742782045994248e0,
203 /* 6 */ 6.579251212010100995060e0,
204 /* 7 */ 8.525161361065414300166e0,
205 /* 8 */ 1.060460290274525022842e1,
206 /* 9 */ 1.280182748008146961121e1,
207 /* 10 */ 1.510441257307551529523e1,
208 /* 11 */ 1.750230784587388583929e1,
209 /* 12 */ 1.998721449566188614952e1,
210 /* 13 */ 2.255216385312342288557e1,
211 /* 14 */ 2.519122118273868150009e1,
212 /* 15 */ 2.789927138384089156609e1,
213 /* 16 */ 3.067186010608067280376e1,
214 /* 17 */ 3.350507345013688888401e1,
215 /* 18 */ 3.639544520803305357622e1,
216 /* 19 */ 3.933988418719949403622e1,
217 /* 20 */ 4.233561646075348502966e1,
218 /* 21 */ 4.538013889847690802616e1,
219 /* 22 */ 4.847118135183522387964e1,
220 /* 23 */ 5.160667556776437357045e1,
221 /* 24 */ 5.478472939811231919009e1,
222 /* 25 */ 5.800360522298051993929e1,
223 /* 26 */ 6.126170176100200198477e1,
224 /* 27 */ 6.455753862700633105895e1,
225 /* 28 */ 6.788974313718153498289e1,
226 /* 29 */ 7.125703896716800901007e1,
227 /* 30 */ 7.465823634883016438549e1,
228 /* 31 */ 7.809222355331531063142e1,
229 /* 32 */ 8.155795945611503717850e1,
230 /* 33 */ 8.505446701758151741396e1,
231 /* 34 */ 8.858082754219767880363e1,
232 /* 35 */ 9.213617560368709248333e1,
233 /* 36 */ 9.571969454214320248496e1,
234 /* 37 */ 9.933061245478742692933e1,
235 /* 38 */ 1.029681986145138126988e2,
236 /* 39 */ 1.066317602606434591262e2,
237 /* 40 */ 1.103206397147573954291e2,
238 /* 41 */ 1.140342117814617032329e2,
239 /* 42 */ 1.177718813997450715388e2,
240 /* 43 */ 1.215330815154386339623e2,
241 /* 44 */ 1.253172711493568951252e2,
242 /* 45 */ 1.291239336391272148826e2,
243 /* 46 */ 1.329525750356163098828e2,
244 /* 47 */ 1.368027226373263684696e2,
245 /* 48 */ 1.406739236482342593987e2,
246 /* 49 */ 1.445657439463448860089e2,
247 /* 50 */ 1.484777669517730320675e2,
248 /* 51 */ 1.524095925844973578392e2,
249 /* 52 */ 1.563608363030787851941e2,
250 /* 53 */ 1.603311282166309070282e2,
251 /* 54 */ 1.643201122631951814118e2,
252 /* 55 */ 1.683274454484276523305e2,
253 /* 56 */ 1.723527971391628015638e2,
254 /* 57 */ 1.763958484069973517152e2,
255 /* 58 */ 1.804562914175437710518e2,
256 /* 59 */ 1.845338288614494905025e2,
257 /* 60 */ 1.886281734236715911873e2,
258 /* 61 */ 1.927390472878449024360e2,
259 /* 62 */ 1.968661816728899939914e2,
260 /* 63 */ 2.010093163992815266793e2,
261 /* 64 */ 2.051681994826411985358e2,
262 /* 65 */ 2.093425867525368356464e2,
263 /* 66 */ 2.135322414945632611913e2,
264 /* 67 */ 2.177369341139542272510e2,
265 /* 68 */ 2.219564418191303339501e2,
266 /* 69 */ 2.261905483237275933323e2,
267 /* 70 */ 2.304390435657769523214e2,
268 /* 71 */ 2.347017234428182677427e2,
269 /* 72 */ 2.389783895618343230538e2,
270 /* 73 */ 2.432688490029827141829e2,
271 /* 74 */ 2.475729140961868839366e2,
272 /* 75 */ 2.518904022097231943772e2,
273 /* 76 */ 2.562211355500095254561e2,
274 /* 77 */ 2.605649409718632093053e2,
275 /* 78 */ 2.649216497985528010421e2,
276 /* 79 */ 2.692910976510198225363e2,
277 /* 80 */ 2.736731242856937041486e2,
278 /* 81 */ 2.780675734403661429141e2,
279 /* 82 */ 2.824742926876303960274e2,
280 /* 83 */ 2.868931332954269939509e2,
281 /* 84 */ 2.913239500942703075662e2,
282 /* 85 */ 2.957666013507606240211e2,
283 /* 86 */ 3.002209486470141317540e2,
284 /* 87 */ 3.046868567656687154726e2,
285 /* 88 */ 3.091641935801469219449e2,
286 /* 89 */ 3.136528299498790617832e2,
287 /* 90 */ 3.181526396202093268500e2,
288 /* 91 */ 3.226634991267261768912e2,
289 /* 92 */ 3.271852877037752172008e2,
290 /* 93 */ 3.317178871969284731381e2,
291 /* 94 */ 3.362611819791984770344e2,
292 /* 95 */ 3.408150588707990178690e2,
293 /* 96 */ 3.453794070622668541074e2,
294 /* 97 */ 3.499541180407702369296e2,
295 /* 98 */ 3.545390855194408088492e2,
296 /* 99 */ 3.591342053695753987760e2,
297 /* 100 */ 3.637393755555634901441e2,
298 /* 101 */ 3.683544960724047495950e2,
299 /* 102 */ 3.729794688856890206760e2,
300 /* 103 */ 3.776141978739186564468e2,
301 /* 104 */ 3.822585887730600291111e2,
302 /* 105 */ 3.869125491232175524822e2,
303 /* 106 */ 3.915759882173296196258e2,
304 /* 107 */ 3.962488170517915257991e2,
305 /* 108 */ 4.009309482789157454921e2,
306 /* 109 */ 4.056222961611448891925e2,
307 /* 110 */ 4.103227765269373054205e2,
308 /* 111 */ 4.150323067282496395563e2,
309 /* 112 */ 4.197508055995447340991e2,
310 /* 113 */ 4.244781934182570746677e2,
311 /* 114 */ 4.292143918666515701285e2,
312 /* 115 */ 4.339593239950148201939e2,
313 /* 116 */ 4.387129141861211848399e2,
314 /* 117 */ 4.434750881209189409588e2,
315 /* 118 */ 4.482457727453846057188e2,
316 /* 119 */ 4.530248962384961351041e2,
317 /* 120 */ 4.578123879812781810984e2,
318 /* 121 */ 4.626081785268749221865e2,
319 /* 122 */ 4.674121995716081787447e2,
320 /* 123 */ 4.722243839269805962399e2,
321 /* 124 */ 4.770446654925856331047e2,
322 /* 125 */ 4.818729792298879342285e2,
323 /* 126 */ 4.867092611368394122258e2,
324 /* 127 */ 4.915534482232980034989e2,
325 /* 128 */ 4.964054784872176206648e2,
326 /* 129 */ 5.012652908915792927797e2,
327 /* 130 */ 5.061328253420348751997e2,
328 /* 131 */ 5.110080226652360267439e2,
329 /* 132 */ 5.158908245878223975982e2,
330 /* 133 */ 5.207811737160441513633e2,
331 /* 134 */ 5.256790135159950627324e2,
332 /* 135 */ 5.305842882944334921812e2,
333 /* 136 */ 5.354969431801695441897e2,
334 /* 137 */ 5.404169241059976691050e2,
335 /* 138 */ 5.453441777911548737966e2,
336 /* 139 */ 5.502786517242855655538e2,
337 /* 140 */ 5.552202941468948698523e2,
338 /* 141 */ 5.601690540372730381305e2,
339 /* 142 */ 5.651248810948742988613e2,
340 /* 143 */ 5.700877257251342061414e2,
341 /* 144 */ 5.750575390247102067619e2,
342 /* 145 */ 5.800342727671307811636e2,
343 /* 146 */ 5.850178793888391176022e2,
344 /* 147 */ 5.900083119756178539038e2,
345 /* 148 */ 5.950055242493819689670e2,
346 /* 149 */ 6.000094705553274281080e2,
347 /* 150 */ 6.050201058494236838580e2,
348 /* 151 */ 6.100373856862386081868e2,
349 /* 152 */ 6.150612662070848845750e2,
350 /* 153 */ 6.200917041284773200381e2,
351 /* 154 */ 6.251286567308909491967e2,
352 /* 155 */ 6.301720818478101958172e2,
353 /* 156 */ 6.352219378550597328635e2,
354 /* 157 */ 6.402781836604080409209e2,
355 /* 158 */ 6.453407786934350077245e2,
356 /* 159 */ 6.504096828956552392500e2,
357 /* 160 */ 6.554848567108890661717e2,
358 /* 161 */ 6.605662610758735291676e2,
359 /* 162 */ 6.656538574111059132426e2,
360 /* 163 */ 6.707476076119126755767e2,
361 /* 164 */ 6.758474740397368739994e2,
362 /* 165 */ 6.809534195136374546094e2,
363 /* 166 */ 6.860654073019939978423e2,
364 /* 167 */ 6.911834011144107529496e2,
365 /* 168 */ 6.963073650938140118743e2,
366 /* 169 */ 7.014372638087370853465e2,
367 /* 170 */ 7.065730622457873471107e2
368 };
369
370 #define N_c_inverfc 34
371
372 static const REAL_T c_inverfc[N_c_inverfc] =
373 {
374 0.91646139826896400000,
375 0.48882664027310800000,
376 0.23172920032340500000,
377 0.12461045461371200000,
378 -0.07288467655856750000,
379 0.26999930867002900000,
380 0.15068904736022300000,
381 0.11606502534161400000,
382 0.49999930343979000000,
383 3.97886080735226000000,
384 0.00112648096188977922,
385 1.05739299623423047e-4,
386 0.00351287146129100025,
387 7.71708358954120939e-4,
388 0.00685649426074558612,
389 0.00339721910367775861,
390 0.01127491693325048700,
391 0.01185981170477711040,
392 0.01429619886978980180,
393 0.03464942077890999220,
394 0.00220995927012179067,
395 0.07434243572417848610,
396 0.10587217794159548800,
397 0.01472979383314851210,
398 0.31684763852013594400,
399 0.71365763586873036400,
400 1.05375024970847138000,
401 1.21448730779995237000,
402 1.16374581931560831000,
403 0.95646497474479900600,
404 0.68626594827409781600,
405 0.43439749233143011500,
406 0.24404451059319093500,
407 0.12078223763524522200
408 };
409
410 #define N_ln1p 21
411
412 static const REAL_T c_ln1p[N_ln1p + 1] =
413 {
414 N_ln1p,
415 1.8657327910677296608121390705e-18,
416 -1.3492637457521938883731579510e-17,
417 9.7089758328248469219003866867e-17,
418 -7.0722150011433276578323272272e-16,
419 5.1107345870861673561462339876e-15,
420 -3.7581977830387938294437434651e-14,
421 2.7291231220549214896095654769e-13,
422 -2.0328515972462118942821556033e-12,
423 1.4844576692270934446023686322e-11,
424 -1.1260499376492049411710290413e-10,
425 8.2751976628812389601561347296e-10,
426 -6.4501969776090319441714445454e-09,
427 4.7743678729400456026672697926e-08,
428 -3.8873813517057343800270917900e-07,
429 2.9004512660400621301999384544e-06,
430 -0.00002553258886105542567601400,
431 0.00019211375164056698287947962,
432 -0.00200215904941415466274422081,
433 0.01517767255690553732382488171,
434 -0.28565398551049742084877469679,
435 2.16647910664395270521272590407
436 };
437
jmvdveer@xs4all.nl