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Text File  |  1992-12-20  |  7KB  |  549 lines

  1. /* Chebyshev approximations to Lyle's tables.
  2.  * The tables themselves are given in the comments.
  3.  */
  4.  
  5. /* rms error 3.4e-8, error[16]=2.7e-7 */
  6. static double lm1[10] = {
  7. -0.0000034729,
  8.  0.0000133884,
  9.  0.0000187733,
  10. -0.0003578840,
  11.  0.0009671247,
  12.  0.0039176720,
  13. -0.0355359033,
  14.  0.0524413612,
  15.  0.5553864593,
  16.  1.5064855057
  17. };
  18.  
  19. /* Published table for m1, 0 <= b/c <= 1, increment 0.05
  20.  * except second item in table is for b/c = 0.025.
  21.  * The other tables below are for the same domain.
  22.  */
  23. /*
  24. 1.041667,
  25. 1.042978,
  26. 1.046862,
  27. 1.062294,
  28. 1.087510,
  29. 1.121795,
  30. 1.164216,
  31. 1.213685,
  32. 1.269024,
  33. 1.329023,
  34. 1.392498,
  35. 1.458333,
  36. 1.525512,
  37. 1.593137,
  38. 1.660442,
  39. 1.726790,
  40. 1.791667,
  41. 1.854675,
  42. 1.915518,
  43. 1.973987,
  44. 2.029950,
  45. 2.083333
  46. */
  47.  
  48. /* rms error 4.8e-6, error[5]=5.0e-5 */
  49. static double lm2[10] = {
  50. -0.0001169260,
  51.  0.0001500950,
  52.  0.0011789118,
  53. -0.0056765335,
  54. -0.0013112684,
  55.  0.0738861156,
  56. -0.1056741543,
  57. -0.6266412368,
  58. -0.5858267544,
  59.  2.2537343007
  60. };
  61. /*
  62. 2.3872,
  63. 2.3913,
  64. 2.4035,
  65. 2.4508,
  66. 2.5237,
  67. 2.6140,
  68. 2.7115,
  69. 2.8057,
  70. 2.8859,
  71. 2.9430,
  72. 2.9694,
  73. 2.9601,
  74. 2.9119,
  75. 2.8239,
  76. 2.6971,
  77. 2.5337,
  78. 2.3372,
  79. 2.1114,
  80. 1.8608,
  81. 1.5898,
  82. 1.3028,
  83. 1.0037,
  84. */
  85.  
  86. /* rms error 3.8e-4, error[12]=-4.7e-3 */
  87. static double lm3[10] = {
  88.  -0.0042606155,
  89.  -0.0010468853,
  90.   0.0446113661,
  91.  -0.0731942602,
  92.  -0.2972370222,
  93.   1.0307506768,
  94.   1.1953246487,
  95.  -4.7029195421,
  96. -10.3484992669,
  97.   9.3066657497
  98. };
  99. /*
  100. 14.97,
  101. 15.01,
  102. 15.13,
  103. 15.59,
  104. 16.25,
  105. 16.96,
  106. 17.56,
  107. 17.91,
  108. 17.89,
  109. 17.42,
  110. 16.49,
  111. 15.11,
  112. 13.36,
  113. 11.33,
  114. 9.11,
  115. 6.83,
  116. 4.58,
  117. 2.44,
  118. 0.48,
  119. -1.24,
  120. -2.69,
  121. -3.85
  122. */
  123.  
  124. /* rms err 2.0e-8, error[4]=2.1e-7 */
  125. static double ll0[14] = {
  126.  0.0000005312,
  127. -0.0000009967,
  128.  0.0000024127,
  129. -0.0000043949,
  130.  0.0000086993,
  131. -0.0000174566,
  132.  0.0000341420,
  133. -0.0000458429,
  134.  0.0000391753,
  135. -0.0008766349,
  136.  0.0103861660,
  137. -0.0608657354,
  138.  0.1636987232,
  139.  0.7359809131
  140. };
  141.  
  142. /*
  143. 0.5,
  144. 0.5252663,
  145. 0.5489951,
  146. 0.5924342,
  147. 0.6310248,
  148. 0.6652018,
  149. 0.6953236,
  150. 0.7217163,
  151. 0.7446891,
  152. 0.7645392,
  153. 0.7815523,
  154. 0.7960019,
  155. 0.8081473,
  156. 0.8182324,
  157. 0.8264842,
  158. 0.8331124,
  159. 0.8383088,
  160. 0.8422476,
  161. 0.8450864,
  162. 0.8469663,
  163. 0.8480134,
  164. 0.8483397
  165. */
  166.  
  167. /* rms error 3.3e08, error[12]=2.9e-7 */
  168. static double ll1[12] = {
  169. -0.0000006228,
  170.  0.0000017514,
  171.  0.0000034603,
  172. -0.0000388956,
  173.  0.0000651590,
  174.  0.0005838149,
  175. -0.0037738396,
  176.  0.0050897845,
  177.  0.0357531842,
  178. -0.1230922762,
  179. -0.6230238402,
  180.  3.2591183517
  181. };
  182. /*
  183. 3.732639,
  184. 3.732506,
  185. 3.731810,
  186. 3.727159,
  187. 3.716052,
  188. 3.696644,
  189. 3.667845,
  190. 3.629250,
  191. 3.581036,
  192. 3.523847,
  193. 3.458662,
  194. 3.386676,
  195. 3.309190,
  196. 3.227522,
  197. 3.142942,
  198. 3.056619,
  199. 2.969599,
  200. 2.882783,
  201. 2.796929,
  202. 2.712655,
  203. 2.630449,
  204. 2.550686
  205. */
  206.  
  207.  
  208. /* rms error 5.8e-6, error[18]=5.4e-5 */
  209. static double ll2[10] = {
  210.  0.0002006024,
  211. -0.0007747556,
  212. -0.0005694527,
  213.  0.0135103091,
  214. -0.0334095624,
  215. -0.0667246939,
  216.  0.4391517110,
  217.  0.1414009803,
  218. -3.1632194405,
  219.  1.3214159925
  220. };
  221. /*
  222. 4.1667,
  223. 4.1614,
  224. 4.1434,
  225. 4.0584,
  226. 3.8971,
  227. 3.6550,
  228. 3.3359,
  229. 2.9510,
  230. 2.5161,
  231. 2.0499,
  232. 1.5715,
  233. 1.0990,
  234. 0.6479,
  235. 0.2308,
  236. -0.1431,
  237. -0.4677,
  238. -0.7400,
  239. -0.9592,
  240. -1.1265,
  241. -1.2448,
  242. -1.3175,
  243. -1.3490
  244. */
  245.  
  246. /* rms error 5.4e-4, error[10]=5.2e-3 */
  247. static double ll3[10] = {
  248.  0.0095823670,
  249. -0.0126747061,
  250. -0.0646408894,
  251.  0.2999226114,
  252. -0.0681630799,
  253. -2.0782285220,
  254.  2.4921454033,
  255.  8.0862929808,
  256. -9.0838699736,
  257.  4.0410431616
  258. };
  259. /*
  260. 17.05,
  261. 17.00,
  262. 16.81,
  263. 15.88,
  264. 14.13,
  265. 11.60,
  266. 8.45,
  267. 4.98,
  268. 1.49,
  269. -1.73,
  270. -4.42,
  271. -6.44,
  272. -7.68,
  273. -8.16,
  274. -7.93,
  275. -7.09,
  276. -5.77,
  277. -4.09,
  278. -2.21,
  279. -0.23,
  280. 1.74,
  281. 3.62
  282. */
  283.  
  284. /* rms error 4.2e-8, error[11]=-5.4e-7 */
  285. static double lm1a[10] = {
  286.  0.0000033780,
  287. -0.0000134754,
  288. -0.0000187875,
  289.  0.0003579377,
  290. -0.0009673040,
  291. -0.0039179989,
  292.  0.0355358520,
  293. -0.0524412952,
  294. -0.5553866352,
  295.  2.6601812765
  296. };
  297. /* Published table for m1, 0 <= c/b <= 1, increment 0.05
  298.  * except second item in table is for c/b = 0.025.
  299.  */
  300. /*
  301. 3.125,
  302. 3.123699,
  303. 3.119805,
  304. 3.104373,
  305. 3.079157,
  306. 3.044872,
  307. 3.002451,
  308. 2.952982,
  309. 2.897643,
  310. 2.837644,
  311. 2.774168,
  312. 2.708333,
  313. 2.641155,
  314. 2.573529,
  315. 2.506224,
  316. 2.439877,
  317. 2.375,
  318. 2.311992,
  319. 2.251149,
  320. 2.192680,
  321. 2.136717,
  322. 2.083333
  323. */
  324.  
  325. /* rms error 5.5e-6, error[13]=-6.6e-5 */
  326. static double lm2a[10] = {
  327. -0.0001538028,
  328.  0.0003005328,
  329.  0.0014141190,
  330. -0.0098646583,
  331.  0.0099736709,
  332.  0.1195762265,
  333. -0.5202566888,
  334. -0.0148097666,
  335.  5.8936719056,
  336. -4.4761545717
  337. };
  338. /*
  339. -9.7656,
  340. -9.7463,
  341. -9.6886,
  342. -9.4613,
  343. -9.0942,
  344. -8.6040,
  345. -8.0115,
  346. -7.3402,
  347. -6.6144,
  348. -5.8573,
  349. -5.0903,
  350. -4.3316,
  351. -3.5961,
  352. -2.8951,
  353. -2.2366,
  354. -1.6260,
  355. -1.0656,
  356. -0.5563,
  357. -0.0970,
  358.  0.3141,
  359.  0.6800,
  360.  1.0037
  361. */
  362. /* rms error 9.3e-4, error[1]=-7.0e-3*/
  363. static double lm3a[8] = {
  364.  -0.0747921450,
  365.   0.2366356004,
  366.   0.2073998920,
  367.  -3.0719280632,
  368.   5.4073000573,
  369.  11.4653879484,
  370. -45.6116695255,
  371.  27.5899097906
  372. };
  373. /*
  374. 76.29,
  375. 76.01
  376. 75.14,
  377. 71.79,
  378. 66.50,
  379. 59.67,
  380. 51.78,
  381. 43.36,
  382. 34.88,
  383. 26.77,
  384. 19.34,
  385. 12.82,
  386. 7.32,
  387. 2.89,
  388. -0.51,
  389. -2.94,
  390. -4.52,
  391. -5.37,
  392. -5.61,
  393. -5.37,
  394. -4.75,
  395. -3.85
  396. */
  397. /* rms error 2.0e-8, error[4]=2.1e-7 */
  398. static double ll0a[14] = {
  399.  0.0000005312,
  400. -0.0000009967,
  401.  0.0000024127,
  402. -0.0000043949,
  403.  0.0000086993,
  404. -0.0000174566,
  405.  0.0000341420,
  406. -0.0000458429,
  407.  0.0000391753,
  408. -0.0008766349,
  409.  0.0103861660,
  410. -0.0608657354,
  411.  0.1636987232,
  412.  0.7359809131
  413. };
  414. /*
  415. 0.5,
  416. 0.5252663
  417. 0.5489951,
  418. 0.5924342,
  419. 0.6310248,
  420. 0.6652018,
  421. 0.6953236,
  422. 0.7217163,
  423. 0.7446891,
  424. 0.7645392,
  425. 0.7815523,
  426. 0.7960019,
  427. 0.8081473,
  428. 0.8182324,
  429. 0.8264842,
  430. 0.8331124,
  431. 0.8383088,
  432. 0.8422476,
  433. 0.8450864,
  434. 0.8469663,
  435. 0.8480134,
  436. 0.8483397
  437. */
  438. /* rms error 4.2e-8, error[13]=-3.9e-7 */
  439. static double ll1a[10] = {
  440. -0.0000082220,
  441.  0.0000262887,
  442.  0.0000667570,
  443. -0.0007981488,
  444.  0.0016823136,
  445.  0.0093955024,
  446. -0.0669376719,
  447.  0.0672334814,
  448.  0.9499148137,
  449.  1.5901108600
  450. };
  451. /*
  452. 0.781250,
  453. 0.783689,
  454. 0.790984,
  455. 0.819830,
  456. 0.866769,
  457. 0.930230,
  458. 1.008207,
  459. 1.098406,
  460. 1.198386,
  461. 1.305696,
  462. 1.417987,
  463. 1.533097,
  464. 1.649113,
  465. 1.764399,
  466. 1.877606,
  467. 1.987664,
  468. 2.093763,
  469. 2.195318,
  470. 2.291944,
  471. 2.383421,
  472. 2.469663,
  473. 2.550686
  474. */
  475. /* rms error 5.8e-6, error[3]=5.7e-5 */
  476. static double ll2a[10] = {
  477.  0.0002543603,
  478. -0.0003568791,
  479. -0.0027957820,
  480.  0.0145977757,
  481. -0.0039745506,
  482. -0.1824652010,
  483.  0.5252161031,
  484.  0.6204189765,
  485. -4.4483986846,
  486.  2.1285089025
  487. };
  488. /*
  489. 6.5104,
  490. 6.4896,
  491. 6.4274,
  492. 6.1838,
  493. 5.7944,
  494. 5.2827,
  495. 4.6774,
  496. 4.0102,
  497. 3.3128,
  498. 2.6145,
  499. 1.9404,
  500. 1.3107,
  501. 0.7400,
  502. 0.2378,
  503. -0.1912,
  504. -0.5460,
  505. -0.8287,
  506. -1.0437,
  507. -1.1966,
  508. -1.2939,
  509. -1.3425,
  510. -1.3490
  511. */
  512. /* rms error 4.2e-4, error[4]=4.3e-3 */
  513. static double ll3a[10] = {
  514.  -0.0087938529,
  515.  -0.0016908604,
  516.   0.1275226249,
  517.  -0.3170188018,
  518.  -0.5340837082,
  519.   4.2395340927,
  520.  -4.7459343890,
  521.  -16.3780190744,
  522.   41.6213541023,
  523.  -20.3831149153
  524. };
  525. /*
  526. -69.30,
  527. -68.94
  528. -67.88,
  529. -63.77,
  530. -57.35,
  531. -49.20,
  532. -39.99,
  533. -30.44,
  534. -21.17,
  535. -12.70,
  536. -5.39,
  537.  0.55,
  538.  5.05,
  539.  8.17,
  540. 10.03,
  541. 10.82,
  542. 10.73,
  543. 9.97,
  544. 8.73,
  545. 7.16,
  546. 5.42,
  547. 3.62
  548. */
  549.