148 lines
6.3 KiB
C
148 lines
6.3 KiB
C
/* Copyright(C) 1996 Takuya OOURA
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You may use, copy, modify this code for any purpose and
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without fee.
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Package home: http://www.kurims.kyoto-u.ac.jp/~ooura/bessel.html
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*/
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/* Bessel I_0(x) function in double precision */
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#include <math.h>
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static double
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dbesi0 (double x)
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{
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int k;
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double w, t, y;
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static double a[65] = {
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8.5246820682016865877e-11, 2.5966600546497407288e-9,
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7.9689994568640180274e-8, 1.9906710409667748239e-6,
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4.0312469446528002532e-5, 6.4499871606224265421e-4,
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0.0079012345761930579108, 0.071111111109207045212,
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0.444444444444724909, 1.7777777777777532045,
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4.0000000000000011182, 3.99999999999999998,
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1.0000000000000000001,
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1.1520919130377195927e-10, 2.2287613013610985225e-9,
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8.1903951930694585113e-8, 1.9821560631611544984e-6,
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4.0335461940910133184e-5, 6.4495330974432203401e-4,
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0.0079013012611467520626, 0.071111038160875566622,
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0.44444450319062699316, 1.7777777439146450067,
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4.0000000132337935071, 3.9999999968569015366,
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1.0000000003426703174,
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1.5476870780515238488e-10, 1.2685004214732975355e-9,
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9.2776861851114223267e-8, 1.9063070109379044378e-6,
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4.0698004389917945832e-5, 6.4370447244298070713e-4,
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0.0079044749458444976958, 0.071105052411749363882,
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0.44445280640924755082, 1.7777694934432109713,
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4.0000055808824003386, 3.9999977081165740932,
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1.0000004333949319118,
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2.0675200625006793075e-10, -6.1689554705125681442e-10,
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1.2436765915401571654e-7, 1.5830429403520613423e-6,
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4.2947227560776583326e-5, 6.3249861665073441312e-4,
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0.0079454472840953930811, 0.070994327785661860575,
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0.44467219586283000332, 1.7774588182255374745,
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4.0003038986252717972, 3.9998233869142057195,
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1.0000472932961288324,
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2.7475684794982708655e-10, -3.8991472076521332023e-9,
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1.9730170483976049388e-7, 5.9651531561967674521e-7,
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5.1992971474748995357e-5, 5.7327338675433770752e-4,
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0.0082293143836530412024, 0.069990934858728039037,
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0.44726764292723985087, 1.7726685170014087784,
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4.0062907863712704432, 3.9952750700487845355,
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1.0016354346654179322
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};
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static double b[70] = {
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6.7852367144945531383e-8, 4.6266061382821826854e-7,
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6.9703135812354071774e-6, 7.6637663462953234134e-5,
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7.9113515222612691636e-4, 0.0073401204731103808981,
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0.060677114958668837046, 0.43994941411651569622,
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2.7420017097661750609, 14.289661921740860534,
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59.820609640320710779, 188.78998681199150629,
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399.8731367825601118, 427.56411572180478514,
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1.8042097874891098754e-7, 1.2277164312044637357e-6,
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1.8484393221474274861e-5, 2.0293995900091309208e-4,
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0.0020918539850246207459, 0.019375315654033949297,
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0.15985869016767185908, 1.1565260527420641724,
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7.1896341224206072113, 37.354773811947484532,
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155.80993164266268457, 489.5211371158540918,
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1030.9147225169564806, 1093.5883545113746958,
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4.8017305613187493564e-7, 3.261317843912380074e-6,
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4.9073137508166159639e-5, 5.3806506676487583755e-4,
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0.0055387918291051866561, 0.051223717488786549025,
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0.42190298621367914765, 3.0463625987357355872,
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18.895299447327733204, 97.915189029455461554,
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407.13940115493494659, 1274.3088990480582632,
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2670.9883037012547506, 2815.7166284662544712,
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1.2789926338424623394e-6, 8.6718263067604918916e-6,
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1.3041508821299929489e-4, 0.001428224737372747892,
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0.014684070635768789378, 0.13561403190404185755,
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1.1152592585977393953, 8.0387088559465389038,
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49.761318895895479206, 257.2684232313529138,
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1066.8543146269566231, 3328.3874581009636362,
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6948.8586598121634874, 7288.4893398212481055,
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3.409350368197032893e-6, 2.3079025203103376076e-5,
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3.4691373283901830239e-4, 0.003794994977222908545,
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0.038974209677945602145, 0.3594948380414878371,
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2.9522878893539528226, 21.246564609514287056,
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131.28727387146173141, 677.38107093296675421,
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2802.3724744545046518, 8718.5731420798254081,
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18141.348781638832286, 18948.925349296308859
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};
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static double c[45] = {
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2.5568678676452702768e-15, 3.0393953792305924324e-14,
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6.3343751991094840009e-13, 1.5041298011833009649e-11,
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4.4569436918556541414e-10, 1.746393051427167951e-8,
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1.0059224011079852317e-6, 1.0729838945088577089e-4,
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0.05150322693642527738,
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5.2527963991711562216e-15, 7.202118481421005641e-15,
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7.2561421229904797156e-13, 1.482312146673104251e-11,
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4.4602670450376245434e-10, 1.7463600061788679671e-8,
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1.005922609132234756e-6, 1.0729838937545111487e-4,
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0.051503226936437300716,
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1.3365917359358069908e-14, -1.2932643065888544835e-13,
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1.7450199447905602915e-12, 1.0419051209056979788e-11,
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4.58047881980598326e-10, 1.7442405450073548966e-8,
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1.0059461453281292278e-6, 1.0729837434500161228e-4,
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0.051503226940658446941,
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5.3771611477352308649e-14, -1.1396193006413731702e-12,
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1.2858641335221653409e-11, -5.9802086004570057703e-11,
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7.3666894305929510222e-10, 1.6731837150730356448e-8,
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1.0070831435812128922e-6, 1.0729733111203704813e-4,
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0.051503227360726294675,
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3.7819492084858931093e-14, -4.8600496888588034879e-13,
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1.6898350504817224909e-12, 4.5884624327524255865e-11,
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1.2521615963377513729e-10, 1.8959658437754727957e-8,
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1.0020716710561353622e-6, 1.073037119856927559e-4,
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0.05150322383300230775
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};
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w = fabs (x);
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if (w < 8.5) {
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t = w * w * 0.0625;
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k = 13 * ((int) t);
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y = (((((((((((a[k] * t + a[k + 1]) * t +
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a[k + 2]) * t + a[k + 3]) * t +
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a[k + 4]) * t + a[k + 5]) * t + a[k +
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6]) * t + a[k + 7]) * t + a[k + 8]) * t + a[k +
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9]) * t + a[k + 10]) * t + a[k + 11]) * t + a[k + 12];
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} else if (w < 12.5) {
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k = (int) w;
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t = w - k;
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k = 14 * (k - 8);
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y = ((((((((((((b[k] * t + b[k + 1]) * t + b[k + 2]) * t + b[k + 3]) * t +
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b[k + 4]) * t + b[k + 5]) * t + b[k +
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6]) * t + b[k + 7]) * t + b[k + 8]) * t +
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b[k + 9]) * t + b[k + 10]) * t + b[k + 11]) * t + b[k +
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12]) * t + b[k + 13];
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} else {
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t = 60 / w;
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k = 9 * ((int) t);
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y = ((((((((c[k] * t + c[k + 1]) * t +
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c[k + 2]) * t + c[k + 3]) * t + c[k + 4]) * t +
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c[k + 5]) * t + c[k + 6]) * t + c[k + 7]) * t +
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c[k + 8]) * sqrt (t) * exp (w);
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}
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return y;
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}
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