File indexing completed on 2024-05-12 05:55:11 

0001 /* floatconst.c: constants for higher math functions */
0002 /*
0003     Copyright (C) 2007, 2008 Wolf Lammen.
0004 
0005     This program is free software; you can redistribute it and/or modify
0006     it under the terms of the GNU General Public License as published by
0007     the Free Software Foundation; either version 2 of the License , or
0008     (at your option) any later version.
0009 
0010     This program is distributed in the hope that it will be useful,
0011     but WITHOUT ANY WARRANTY; without even the implied warranty of
0012     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0013     GNU General Public License for more details.
0014 
0015     You should have received a copy of the GNU General Public License
0016     along with this program; see the file COPYING.  If not, write to:
0017 
0018       The Free Software Foundation, Inc.
0019       59 Temple Place, Suite 330
0020       Boston, MA 02111-1307 USA.
0021 
0022 
0023     You may contact the author by:
0024        e-mail:  ookami1 <at> gmx <dot> de
0025        mail:  Wolf Lammen
0026               Oertzweg 45
0027               22307 Hamburg
0028               Germany
0029 
0030 *************************************************************************/
0031 
0032 #include "floatconst.h"
0033 
0034 static char sExp[] =
0035 "2.7182818284""5904523536""0287471352""6624977572""4709369995"
0036   "9574966967""6277240766""3035354759""4571382178""5251664274"
0037   "2746639193""2003059921""8174135966""2904357290""0334295260"
0038   "5956307381""3232862794""3490763233""8298807531""9525101901"
0039   "1573834187";
0040 
0041 static char sLn2[] =
0042 "0.6931471805""5994530941""7232121458""1765680755""0013436025"
0043   "5254120680""0094933936""2196969471""5605863326""9964186875"
0044   "4200148102""0570685734";
0045 
0046 static char sLn3[] =
0047 "1.0986122886""6810969139""5245236922""5257046474""9055782274"
0048   "9451734694""3336374942""9321860896""6873615754""8137320887"
0049   "8797002906""5957865742";
0050 
0051 static char sLn7[] =
0052 "1.9459101490""5531330510""5352743443""1797296370""8472958186"
0053   "1188459390""1499375798""6275206926""7787658498""5878715269"
0054   "9306169420""5851140912";
0055 
0056 static char sLn10[] =
0057 "2.3025850929""9404568401""7991454684""3642076011""0148862877"
0058   "2976033327""9009675726""0967735248""0235997205""0895982983"
0059   "4196778404""2286248633";
0060 
0061 static char sPhi[] =
0062 "1.6180339887""4989484820""4586834365""6381177203""0917980576"
0063   "2862135448""6227052604""6281890244""9707207204""1893911374"
0064   "8475408807""5386891752""1266338622""2353693179""3180060766"
0065   "7263544333""8908659593""9582905638""3226613199""2829026788"
0066   "0675208766";
0067 
0068 static char sPi[] =
0069 "3.1415926535""8979323846""2643383279""5028841971""6939937510"
0070   "5820974944""5923078164""0628620899""8628034825""3421170679"
0071   "8214808651""3282306647""0938446095""5058223172""5359408128"
0072   "4811174502""8410270193""8521105559""6446229489""5493038196"
0073   "4428810976";
0074 
0075 static char sPiDiv2[] =
0076 "1.5707963267""9489661923""1321691639""7514420985""8469968755"
0077   "2910487472""2961539082""0314310449""9314017412""6710585339"
0078   "9107404325""6641153324";
0079 
0080 static char sPiDiv4[] =
0081 "0.7853981633""9744830961""5660845819""8757210492""9234984377"
0082   "6455243736""1480769541""0157155224""9657008706""3355292669"
0083   "9553702162""8320576662";
0084 
0085 static char s2Pi[] =
0086 "6.2831853071""7958647692""5286766559""0057683943""3879875021"
0087   "1641949889""1846156328""1257241799""7256069650""6842341359"
0088   "6429617302""6564613294";
0089 
0090 static char s1DivPi[] =
0091 "0.3183098861""8379067153""7767526745""0287240689""1929148091"
0092   "2897495334""6881177935""9526845307""0180227605""5325061719"
0093   "1214568545""3515916074";
0094 
0095 static char sLnSqrt2PiMinusHalf[] =
0096 "0.4189385332""0467274178""0329736405""6176398613""9747363778"
0097   "3412817151""5404827656""9592726039""7694743298""6359541976"
0098   "2200564662""4634337446";
0099 
0100 static char sSqrtPi[] =
0101 "1.7724538509""0551602729""8167483341""1451827975""4945612238"
0102   "7128213807""7898529112""8459103218""1374950656""7385446654"
0103   "1622682362""4282570666";
0104 
0105 static char s1DivSqrtPi[] =
0106 "0.5641895835""4775628694""8079451560""7725858440""5062932899"
0107   "8856844085""7217106424""6844149341""4486743660""2021073634"
0108   "4302834790""6361707352";
0109 
0110 static char s2DivSqrtPi[] =
0111 "1.1283791670""9551257389""6158903121""5451716881""0125865799"
0112   "7713688171""4434212849""3688298682""8973487320""4042147268"
0113   "8605669581""2723414703";
0114 
0115 static char* sBernoulli[] =
0116 {
0117 "1",
0118 "6",
0119 "1",
0120 "-30",
0121 "1",
0122 "42",
0123 "1",
0124 "-30",
0125 "5",
0126 "66",
0127 "691",
0128 "-2730",
0129 "7",
0130 "6",
0131 "3617",
0132 "-510",
0133 "43867",
0134 "798",
0135 "174611",
0136 "-330",
0137 "854513",
0138 "138",
0139 "236364091",
0140 "-2730",
0141 "8553103",
0142 "6",
0143 "23749461029",
0144 "-870",
0145 "8615841276005",
0146 "14322",
0147 "7709321041217",
0148 "-510",
0149 "2577687858367",
0150 "6",
0151 "26315271553053477373",
0152 "-1919190",
0153 "2929993913841559",
0154 "6",
0155 "261082718496449122051",
0156 "-13530",
0157 "1520097643918070802691",
0158 "1806",
0159 "27833269579301024235023",
0160 "-690",
0161 "596451111593912163277961",
0162 "282",
0163 "5609403368997817686249127547",
0164 "-46410",
0165 "495057205241079648212477525",
0166 "66",
0167 "801165718135489957347924991853",
0168 "-1590",
0169 "29149963634884862421418123812691",
0170 "798",
0171 "2479392929313226753685415739663229",
0172 "-870",
0173 "84483613348880041862046775994036021",
0174 "354",
0175 "1215233140483755572040304994079820246041491",
0176 "-56786730",
0177 "12300585434086858541953039857403386151",
0178 "6",
0179 "106783830147866529886385444979142647942017",
0180 "-510",
0181 "1472600022126335654051619428551932342241899101",
0182 "64722",
0183 "78773130858718728141909149208474606244347001",
0184 "-30",
0185 "1505381347333367003803076567377857208511438160235",
0186 "4686",
0187 "5827954961669944110438277244641067365282488301844260429",
0188 "-140100870",
0189 "34152417289221168014330073731472635186688307783087",
0190 "6",
0191 "24655088825935372707687196040585199904365267828865801",
0192 "-30",
0193 "414846365575400828295179035549542073492199375372400483487",
0194 "3318",
0195 "4603784299479457646935574969019046849794257872751288919656867",
0196 "-230010",
0197 "1677014149185145836823154509786269900207736027570253414881613",
0198 "498",
0199 "2024576195935290360231131160111731009989917391198090877281083932477",
0200 "-3404310",
0201 "660714619417678653573847847426261496277830686653388931761996983",
0202 "6",
0203 "1311426488674017507995511424019311843345750275572028644296919890574047",
0204 "-61410",
0205 "1179057279021082799884123351249215083775254949669647116231545215727922535",
0206 "272118",
0207 "1295585948207537527989427828538576749659341483719435143023316326829946247",
0208 "-1410",
0209 "1220813806579744469607301679413201203958508415202696621436215105284649447",
0210 "6",
0211 "-4.70038339580357310785752555350060606545967373697590579151397635641e73",
0212 "1",
0213 "1.13180434454842492706751862577339342678903659547507479181789935417e76",
0214 "1",
0215 "-2.83822495706937069592641563364817647382846809280128821282285317145e78",
0216 "1",
0217 "7.40642489796788506297508271409209841768797317880887066731161003487e80",
0218 "1",
0219 "-2.00964548027566044834656196727153631868672708225328766243461301989e83",
0220 "1",
0221 "5.66571700508059414457193460305193569614194682875104206213875644522e85",
0222 "1",
0223 "-1.65845111541362169158237133743199123014949626147254647274024668156e88",
0224 "1",
0225 "5.03688599504923774192894219151801548124423742649032141415256513225e90",
0226 "1",
0227 "-1.58614682376581863693634015729664387827409784127789638804728645143e93",
0228 "1",
0229 "5.17567436175456269840732406825071225612408492359305508590621669403e95",
0230 "1",
0231 "-1.74889218402171173396900258776181591451414761618265448726273472159e98",
0232 "1",
0233 "6.11605199949521852558245252642641677807677268467832007168432401127e100",
0234 "1",
0235 "-2.2122776912707834942288323456712932445573185054987780150566552693e103",
0236 "1",
0237 "8.27227767987709698542210624599845957312046505184335662838488529886e105",
0238 "1",
0239 "-3.19589251114157095835916343691808148735262766710991122731845042431e108",
0240 "1",
0241 "1.27500822233877929823100243029266798669571917963897732951605857354e111",
0242 "1",
0243 "-5.25009230867741338994028246245651754469198940377552432607801345222e113",
0244 "1",
0245 "2.2301817894241625209869298198838728143738272150875878542490550781e116",
0246 "1",
0247 "-9.76845219309552044386335133989802393011669026749856789710001706619e118",
0248 "1",
0249 "4.40983619784529542722726228748131691918757542655281147353197591401e121",
0250 "1",
0251 "-2.05085708864640888397293377275830154864565966904008359530873982755e124",
0252 "1"
0253 };
0254 
0255 floatstruct cBernoulliNum[68];
0256 floatstruct cBernoulliDen[68];
0257 
0258 floatstruct c1;
0259 floatstruct c2;
0260 floatstruct c3;
0261 floatstruct c12;
0262 floatstruct c16;
0263 floatstruct cExp;
0264 floatstruct cMinus1;
0265 floatstruct cMinus20;
0266 floatstruct c1Div2;
0267 floatstruct cLn2;
0268 floatstruct cLn3;
0269 floatstruct cLn7;
0270 floatstruct cLn10;
0271 floatstruct cPhi;
0272 floatstruct cPi;
0273 floatstruct cPiDiv2;
0274 floatstruct cPiDiv4;
0275 floatstruct c2Pi;
0276 floatstruct c1DivPi;
0277 floatstruct cSqrtPi;
0278 floatstruct cLnSqrt2PiMinusHalf;
0279 floatstruct c1DivSqrtPi;
0280 floatstruct c2DivSqrtPi;
0281 floatstruct cMinus0_4;
0282 floatstruct cUnsignedBound;
0283 
0284 int erfcdigits = 0;
0285 floatstruct erfccoeff[MAXERFCIDX];
0286 floatstruct erfcalpha;
0287 floatstruct erfcalphasqr;
0288 floatstruct erfct2;
0289 floatstruct erfct3;
0290 
0291 void
0292 floatmath_init()
0293 {
0294   int i, save;
0295   floatnum_init();
0296 
0297   save = float_setprecision(MAXDIGITS);
0298   float_create(&c1);
0299   float_setinteger(&c1, 1);
0300   float_create(&c2);
0301   float_setinteger(&c2, 2);
0302   float_create(&c3);
0303   float_setinteger(&c3, 3);
0304   float_create(&c12);
0305   float_setinteger(&c12, 12);
0306   float_create(&c16);
0307   float_setinteger(&c16, 16);
0308   float_create(&cMinus1);
0309   float_setinteger(&cMinus1, -1);
0310   float_create(&cMinus20);
0311   float_setinteger(&cMinus20, -20);
0312   float_create(&c1Div2);
0313   float_setscientific(&c1Div2, ".5", NULLTERMINATED);
0314   float_create(&cExp);
0315   float_setscientific(&cExp, sExp, NULLTERMINATED);
0316   float_create(&cLn2);
0317   float_setscientific(&cLn2, sLn2, NULLTERMINATED);
0318   float_create(&cLn3);
0319   float_setscientific(&cLn3, sLn3, NULLTERMINATED);
0320   float_create(&cLn7);
0321   float_setscientific(&cLn7, sLn7, NULLTERMINATED);
0322   float_create(&cLn10);
0323   float_setscientific(&cLn10, sLn10, NULLTERMINATED);
0324   float_create(&cPhi);
0325   float_setscientific(&cPhi, sPhi, NULLTERMINATED);
0326   float_create(&cPi);
0327   float_setscientific(&cPi, sPi, NULLTERMINATED);
0328   float_create(&cPiDiv2);
0329   float_setscientific(&cPiDiv2, sPiDiv2, NULLTERMINATED);
0330   float_create(&cPiDiv4);
0331   float_setscientific(&cPiDiv4, sPiDiv4, NULLTERMINATED);
0332   float_create(&c2Pi);
0333   float_setscientific(&c2Pi, s2Pi, NULLTERMINATED);
0334   float_create(&c1DivPi);
0335   float_setscientific(&c1DivPi, s1DivPi, NULLTERMINATED);
0336   float_create(&cSqrtPi);
0337   float_setscientific(&cSqrtPi, sSqrtPi, NULLTERMINATED);
0338   float_create(&cLnSqrt2PiMinusHalf);
0339   float_setscientific(&cLnSqrt2PiMinusHalf, sLnSqrt2PiMinusHalf,
0340                       NULLTERMINATED);
0341   float_create(&c1DivSqrtPi);
0342   float_setscientific(&c1DivSqrtPi, s1DivSqrtPi, NULLTERMINATED);
0343   float_create(&c2DivSqrtPi);
0344   float_setscientific(&c2DivSqrtPi, s2DivSqrtPi, NULLTERMINATED);
0345   float_create(&cMinus0_4);
0346   float_setscientific(&cMinus0_4, "-.4", NULLTERMINATED);
0347   for (i = -1; ++i < MAXBERNOULLIIDX;)
0348   {
0349     float_create(&cBernoulliNum[i]);
0350     float_create(&cBernoulliDen[i]);
0351     float_setscientific(&cBernoulliNum[i], sBernoulli[2*i], NULLTERMINATED);
0352     float_setscientific(&cBernoulliDen[i], sBernoulli[2*i+1], NULLTERMINATED);
0353   }
0354   float_create(&cUnsignedBound);
0355   float_copy(&cUnsignedBound, &c1, EXACT);
0356   for (i = -1; ++i < 2*(int)sizeof(unsigned);)
0357     float_mul(&cUnsignedBound, &c16, &cUnsignedBound, EXACT);
0358   for (i = -1; ++i < MAXERFCIDX;)
0359     float_create(&erfccoeff[i]);
0360   float_create(&erfcalpha);
0361   float_create(&erfcalphasqr);
0362   float_create(&erfct2);
0363   float_create(&erfct3);
0364   float_setprecision(save);
0365 }
0366 
0367 void
0368 floatmath_exit()
0369 {
0370   int i;
0371 
0372   float_free(&c1);
0373   float_free(&c2);
0374   float_free(&c3);
0375   float_free(&c12);
0376   float_free(&c16);
0377   float_free(&cMinus1);
0378   float_free(&cMinus20);
0379   float_free(&c1Div2);
0380   float_free(&cExp);
0381   float_free(&cLn2);
0382   float_free(&cLn3);
0383   float_free(&cLn7);
0384   float_free(&cLn10);
0385   float_free(&cPhi);
0386   float_free(&cPi);
0387   float_free(&cPiDiv2);
0388   float_free(&cPiDiv4);
0389   float_free(&c2Pi);
0390   float_free(&c1DivPi);
0391   float_free(&cSqrtPi);
0392   float_free(&cLnSqrt2PiMinusHalf);
0393   float_free(&c1DivSqrtPi);
0394   float_free(&c2DivSqrtPi);
0395   float_free(&cMinus0_4);
0396   for (i = -1; ++i < MAXBERNOULLIIDX;)
0397   {
0398     float_free(&cBernoulliNum[i]);
0399     float_free(&cBernoulliDen[i]);
0400   }
0401   float_free(&cUnsignedBound);
0402   for (i = -1; ++i < MAXERFCIDX;)
0403     float_free(&erfccoeff[i]);
0404   float_free(&erfcalpha);
0405   float_free(&erfcalphasqr);
0406   float_free(&erfct2);
0407   float_free(&erfct3);
0408 }