maths/tables.c

   1 /*
   2 THE COMPUTER CODE CONTAINED HEREIN IS THE SOLE PROPERTY OF PARALLAX
   3 SOFTWARE CORPORATION ("PARALLAX").  PARALLAX, IN DISTRIBUTING THE CODE TO
   4 END-USERS, AND SUBJECT TO ALL OF THE TERMS AND CONDITIONS HEREIN, GRANTS A
   5 ROYALTY-FREE, PERPETUAL LICENSE TO SUCH END-USERS FOR USE BY SUCH END-USERS
   6 IN USING, DISPLAYING,  AND CREATING DERIVATIVE WORKS THEREOF, SO LONG AS
   7 SUCH USE, DISPLAY OR CREATION IS FOR NON-COMMERCIAL, ROYALTY OR REVENUE
   8 FREE PURPOSES.  IN NO EVENT SHALL THE END-USER USE THE COMPUTER CODE
   9 CONTAINED HEREIN FOR REVENUE-BEARING PURPOSES.  THE END-USER UNDERSTANDS
  10 AND AGREES TO THE TERMS HEREIN AND ACCEPTS THE SAME BY USE OF THIS FILE.
  11 COPYRIGHT 1993-1998 PARALLAX SOFTWARE CORPORATION.  ALL RIGHTS RESERVED.
  12 */
  13
  14 /*
  15  *
  16  * C version of fixed point library
  17  *
  18  */
  19
  20 #ifdef HAVE_CONFIG_H
  21 #include <conf.h>
  22 #endif
  23
  24 #include "maths.h"
  25
  26 ubyte guess_table[] = {
  27         1,
  28         1,1,1,
  29         2,2,2,2,2,
  30         3,3,3,3,3,3,3,
  31         4,4,4,4,4,4,4,4,4,
  32         5,5,5,5,5,5,5,5,5,5,5,
  33         6,6,6,6,6,6,6,6,6,6,6,6,6,
  34         7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
  35         8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
  36         9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
  37         10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
  38         11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
  39         12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,
  40         13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,
  41         14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,
  42         15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15
  43 };
  44
  45 short sincos_table[] = {
  46         0,
  47         402,
  48         804,
  49         1205,
  50         1606,
  51         2006,
  52         2404,
  53         2801,
  54         3196,
  55         3590,
  56         3981,
  57         4370,
  58         4756,
  59         5139,
  60         5520,
  61         5897,
  62         6270,
  63         6639,
  64         7005,
  65         7366,
  66         7723,
  67         8076,
  68         8423,
  69         8765,
  70         9102,
  71         9434,
  72         9760,
  73         10080,
  74         10394,
  75         10702,
  76         11003,
  77         11297,
  78         11585,
  79         11866,
  80         12140,
  81         12406,
  82         12665,
  83         12916,
  84         13160,
  85         13395,
  86         13623,
  87         13842,
  88         14053,
  89         14256,
  90         14449,
  91         14635,
  92         14811,
  93         14978,
  94         15137,
  95         15286,
  96         15426,
  97         15557,
  98         15679,
  99         15791,
 100         15893,
 101         15986,
 102         16069,
 103         16143,
 104         16207,
 105         16261,
 106         16305,
 107         16340,
 108         16364,
 109         16379,
 110         // cos_table
 111         16384,
 112         16379,
 113         16364,
 114         16340,
 115         16305,
 116         16261,
 117         16207,
 118         16143,
 119         16069,
 120         15986,
 121         15893,
 122         15791,
 123         15679,
 124         15557,
 125         15426,
 126         15286,
 127         15137,
 128         14978,
 129         14811,
 130         14635,
 131         14449,
 132         14256,
 133         14053,
 134         13842,
 135         13623,
 136         13395,
 137         13160,
 138         12916,
 139         12665,
 140         12406,
 141         12140,
 142         11866,
 143         11585,
 144         11297,
 145         11003,
 146         10702,
 147         10394,
 148         10080,
 149         9760,
 150         9434,
 151         9102,
 152         8765,
 153         8423,
 154         8076,
 155         7723,
 156         7366,
 157         7005,
 158         6639,
 159         6270,
 160         5897,
 161         5520,
 162         5139,
 163         4756,
 164         4370,
 165         3981,
 166         3590,
 167         3196,
 168         2801,
 169         2404,
 170         2006,
 171         1606,
 172         1205,
 173         804,
 174         402,
 175         0,
 176         -402,
 177         -804,
 178         -1205,
 179         -1606,
 180         -2006,
 181         -2404,
 182         -2801,
 183         -3196,
 184         -3590,
 185         -3981,
 186         -4370,
 187         -4756,
 188         -5139,
 189         -5520,
 190         -5897,
 191         -6270,
 192         -6639,
 193         -7005,
 194         -7366,
 195         -7723,
 196         -8076,
 197         -8423,
 198         -8765,
 199         -9102,
 200         -9434,
 201         -9760,
 202         -10080,
 203         -10394,
 204         -10702,
 205         -11003,
 206         -11297,
 207         -11585,
 208         -11866,
 209         -12140,
 210         -12406,
 211         -12665,
 212         -12916,
 213         -13160,
 214         -13395,
 215         -13623,
 216         -13842,
 217         -14053,
 218         -14256,
 219         -14449,
 220         -14635,
 221         -14811,
 222         -14978,
 223         -15137,
 224         -15286,
 225         -15426,
 226         -15557,
 227         -15679,
 228         -15791,
 229         -15893,
 230         -15986,
 231         -16069,
 232         -16143,
 233         -16207,
 234         -16261,
 235         -16305,
 236         -16340,
 237         -16364,
 238         -16379,
 239         -16384,
 240         -16379,
 241         -16364,
 242         -16340,
 243         -16305,
 244         -16261,
 245         -16207,
 246         -16143,
 247         -16069,
 248         -15986,
 249         -15893,
 250         -15791,
 251         -15679,
 252         -15557,
 253         -15426,
 254         -15286,
 255         -15137,
 256         -14978,
 257         -14811,
 258         -14635,
 259         -14449,
 260         -14256,
 261         -14053,
 262         -13842,
 263         -13623,
 264         -13395,
 265         -13160,
 266         -12916,
 267         -12665,
 268         -12406,
 269         -12140,
 270         -11866,
 271         -11585,
 272         -11297,
 273         -11003,
 274         -10702,
 275         -10394,
 276         -10080,
 277         -9760,
 278         -9434,
 279         -9102,
 280         -8765,
 281         -8423,
 282         -8076,
 283         -7723,
 284         -7366,
 285         -7005,
 286         -6639,
 287         -6270,
 288         -5897,
 289         -5520,
 290         -5139,
 291         -4756,
 292         -4370,
 293         -3981,
 294         -3590,
 295         -3196,
 296         -2801,
 297         -2404,
 298         -2006,
 299         -1606,
 300         -1205,
 301         -804,
 302         -402,
 303         0,
 304         402,
 305         804,
 306         1205,
 307         1606,
 308         2006,
 309         2404,
 310         2801,
 311         3196,
 312         3590,
 313         3981,
 314         4370,
 315         4756,
 316         5139,
 317         5520,
 318         5897,
 319         6270,
 320         6639,
 321         7005,
 322         7366,
 323         7723,
 324         8076,
 325         8423,
 326         8765,
 327         9102,
 328         9434,
 329         9760,
 330         10080,
 331         10394,
 332         10702,
 333         11003,
 334         11297,
 335         11585,
 336         11866,
 337         12140,
 338         12406,
 339         12665,
 340         12916,
 341         13160,
 342         13395,
 343         13623,
 344         13842,
 345         14053,
 346         14256,
 347         14449,
 348         14635,
 349         14811,
 350         14978,
 351         15137,
 352         15286,
 353         15426,
 354         15557,
 355         15679,
 356         15791,
 357         15893,
 358         15986,
 359         16069,
 360         16143,
 361         16207,
 362         16261,
 363         16305,
 364         16340,
 365         16364,
 366         16379,
 367         16384
 368 };
 369
 370 ushort asin_table[] = {
 371         0,
 372         41,
 373         81,
 374         122,
 375         163,
 376         204,
 377         244,
 378         285,
 379         326,
 380         367,
 381         408,
 382         448,
 383         489,
 384         530,
 385         571,
 386         612,
 387         652,
 388         693,
 389         734,
 390         775,
 391         816,
 392         857,
 393         897,
 394         938,
 395         979,
 396         1020,
 397         1061,
 398         1102,
 399         1143,
 400         1184,
 401         1225,
 402         1266,
 403         1307,
 404         1348,
 405         1389,
 406         1431,
 407         1472,
 408         1513,
 409         1554,
 410         1595,
 411         1636,
 412         1678,
 413         1719,
 414         1760,
 415         1802,
 416         1843,
 417         1884,
 418         1926,
 419         1967,
 420         2009,
 421         2050,
 422         2092,
 423         2134,
 424         2175,
 425         2217,
 426         2259,
 427         2300,
 428         2342,
 429         2384,
 430         2426,
 431         2468,
 432         2510,
 433         2551,
 434         2593,
 435         2636,
 436         2678,
 437         2720,
 438         2762,
 439         2804,
 440         2847,
 441         2889,
 442         2931,
 443         2974,
 444         3016,
 445         3059,
 446         3101,
 447         3144,
 448         3187,
 449         3229,
 450         3272,
 451         3315,
 452         3358,
 453         3401,
 454         3444,
 455         3487,
 456         3530,
 457         3573,
 458         3617,
 459         3660,
 460         3704,
 461         3747,
 462         3791,
 463         3834,
 464         3878,
 465         3922,
 466         3965,
 467         4009,
 468         4053,
 469         4097,
 470         4142,
 471         4186,
 472         4230,
 473         4275,
 474         4319,
 475         4364,
 476         4408,
 477         4453,
 478         4498,
 479         4543,
 480         4588,
 481         4633,
 482         4678,
 483         4723,
 484         4768,
 485         4814,
 486         4859,
 487         4905,
 488         4951,
 489         4997,
 490         5043,
 491         5089,
 492         5135,
 493         5181,
 494         5228,
 495         5274,
 496         5321,
 497         5367,
 498         5414,
 499         5461,
 500         5508,
 501         5556,
 502         5603,
 503         5651,
 504         5698,
 505         5746,
 506         5794,
 507         5842,
 508         5890,
 509         5938,
 510         5987,
 511         6035,
 512         6084,
 513         6133,
 514         6182,
 515         6231,
 516         6281,
 517         6330,
 518         6380,
 519         6430,
 520         6480,
 521         6530,
 522         6580,
 523         6631,
 524         6681,
 525         6732,
 526         6783,
 527         6835,
 528         6886,
 529         6938,
 530         6990,
 531         7042,
 532         7094,
 533         7147,
 534         7199,
 535         7252,
 536         7306,
 537         7359,
 538         7413,
 539         7466,
 540         7521,
 541         7575,
 542         7630,
 543         7684,
 544         7740,
 545         7795,
 546         7851,
 547         7907,
 548         7963,
 549         8019,
 550         8076,
 551         8133,
 552         8191,
 553         8249,
 554         8307,
 555         8365,
 556         8424,
 557         8483,
 558         8543,
 559         8602,
 560         8663,
 561         8723,
 562         8784,
 563         8846,
 564         8907,
 565         8970,
 566         9032,
 567         9095,
 568         9159,
 569         9223,
 570         9288,
 571         9353,
 572         9418,
 573         9484,
 574         9551,
 575         9618,
 576         9686,
 577         9754,
 578         9823,
 579         9892,
 580         9963,
 581         10034,
 582         10105,
 583         10177,
 584         10251,
 585         10324,
 586         10399,
 587         10475,
 588         10551,
 589         10628,
 590         10706,
 591         10785,
 592         10866,
 593         10947,
 594         11029,
 595         11113,
 596         11198,
 597         11284,
 598         11371,
 599         11460,
 600         11550,
 601         11642,
 602         11736,
 603         11831,
 604         11929,
 605         12028,
 606         12130,
 607         12234,
 608         12340,
 609         12449,
 610         12561,
 611         12677,
 612         12796,
 613         12919,
 614         13046,
 615         13178,
 616         13315,
 617         13459,
 618         13610,
 619         13770,
 620         13939,
 621         14121,
 622         14319,
 623         14538,
 624         14786,
 625         15079,
 626         15462,
 627         16384,
 628         16384   // extra for when exactly 1
 629 };
 630
 631 ushort acos_table[] = {
 632         16384,
 633         16343,
 634         16303,
 635         16262,
 636         16221,
 637         16180,
 638         16140,
 639         16099,
 640         16058,
 641         16017,
 642         15976,
 643         15936,
 644         15895,
 645         15854,
 646         15813,
 647         15772,
 648         15732,
 649         15691,
 650         15650,
 651         15609,
 652         15568,
 653         15527,
 654         15487,
 655         15446,
 656         15405,
 657         15364,
 658         15323,
 659         15282,
 660         15241,
 661         15200,
 662         15159,
 663         15118,
 664         15077,
 665         15036,
 666         14995,
 667         14953,
 668         14912,
 669         14871,
 670         14830,
 671         14789,
 672         14748,
 673         14706,
 674         14665,
 675         14624,
 676         14582,
 677         14541,
 678         14500,
 679         14458,
 680         14417,
 681         14375,
 682         14334,
 683         14292,
 684         14250,
 685         14209,
 686         14167,
 687         14125,
 688         14084,
 689         14042,
 690         14000,
 691         13958,
 692         13916,
 693         13874,
 694         13833,
 695         13791,
 696         13748,
 697         13706,
 698         13664,
 699         13622,
 700         13580,
 701         13537,
 702         13495,
 703         13453,
 704         13410,
 705         13368,
 706         13325,
 707         13283,
 708         13240,
 709         13197,
 710         13155,
 711         13112,
 712         13069,
 713         13026,
 714         12983,
 715         12940,
 716         12897,
 717         12854,
 718         12811,
 719         12767,
 720         12724,
 721         12680,
 722         12637,
 723         12593,
 724         12550,
 725         12506,
 726         12462,
 727         12419,
 728         12375,
 729         12331,
 730         12287,
 731         12242,
 732         12198,
 733         12154,
 734         12109,
 735         12065,
 736         12020,
 737         11976,
 738         11931,
 739         11886,
 740         11841,
 741         11796,
 742         11751,
 743         11706,
 744         11661,
 745         11616,
 746         11570,
 747         11525,
 748         11479,
 749         11433,
 750         11387,
 751         11341,
 752         11295,
 753         11249,
 754         11203,
 755         11156,
 756         11110,
 757         11063,
 758         11017,
 759         10970,
 760         10923,
 761         10876,
 762         10828,
 763         10781,
 764         10733,
 765         10686,
 766         10638,
 767         10590,
 768         10542,
 769         10494,
 770         10446,
 771         10397,
 772         10349,
 773         10300,
 774         10251,
 775         10202,
 776         10153,
 777         10103,
 778         10054,
 779         10004,
 780         9954,
 781         9904,
 782         9854,
 783         9804,
 784         9753,
 785         9703,
 786         9652,
 787         9601,
 788         9549,
 789         9498,
 790         9446,
 791         9394,
 792         9342,
 793         9290,
 794         9237,
 795         9185,
 796         9132,
 797         9078,
 798         9025,
 799         8971,
 800         8918,
 801         8863,
 802         8809,
 803         8754,
 804         8700,
 805         8644,
 806         8589,
 807         8533,
 808         8477,
 809         8421,
 810         8365,
 811         8308,
 812         8251,
 813         8193,
 814         8135,
 815         8077,
 816         8019,
 817         7960,
 818         7901,
 819         7841,
 820         7782,
 821         7721,
 822         7661,
 823         7600,
 824         7538,
 825         7477,
 826         7414,
 827         7352,
 828         7289,
 829         7225,
 830         7161,
 831         7096,
 832         7031,
 833         6966,
 834         6900,
 835         6833,
 836         6766,
 837         6698,
 838         6630,
 839         6561,
 840         6492,
 841         6421,
 842         6350,
 843         6279,
 844         6207,
 845         6133,
 846         6060,
 847         5985,
 848         5909,
 849         5833,
 850         5756,
 851         5678,
 852         5599,
 853         5518,
 854         5437,
 855         5355,
 856         5271,
 857         5186,
 858         5100,
 859         5013,
 860         4924,
 861         4834,
 862         4742,
 863         4648,
 864         4553,
 865         4455,
 866         4356,
 867         4254,
 868         4150,
 869         4044,
 870         3935,
 871         3823,
 872         3707,
 873         3588,
 874         3465,
 875         3338,
 876         3206,
 877         3069,
 878         2925,
 879         2774,
 880         2614,
 881         2445,
 882         2263,
 883         2065,
 884         1846,
 885         1598,
 886         1305,
 887         922,
 888         0,
 889         0   // extra for when exactly 1
 890 };
 891
 892 fix isqrt_guess_table[] = {
 893         // 0,
 894         0x80000000,
 895         16777216,11863283,9686330,8388608,7502999,6849269,6341191,
 896         5931641,5592405,5305421,5058520,4843165,4653162,4483899,4331858,
 897         4194304,4069072,3954427,3848957,3751499,3661088,3576914,3498291,
 898         3424634,3355443,3290282,3228776,3170595,3115450,3063086,3013276,
 899         2965820,2920538,2877268,2835867,2796202,2758157,2721623,2686504,
 900         2652710,2620160,2588780,2558501,2529260,2500999,2473665,2447208,
 901         2421582,2396745,2372656,2349280,2326581,2304527,2283089,2262239,
 902         2241949,2222196,2202956,2184207,2165929,2148102,2130708,2113730,
 903         2097152,2080957,2065132,2049663,2034536,2019739,2005260,1991089,
 904         1977213,1963624,1950311,1937266,1924478,1911941,1899645,1887584,
 905         1875749,1864135,1852733,1841538,1830544,1819744,1809133,1798706,
 906         1788457,1778381,1768473,1758730,1749145,1739716,1730437,1721306,
 907         1712317,1703468,1694754,1686173,1677721,1669395,1661191,1653108,
 908         1645141,1637288,1629547,1621914,1614388,1606965,1599644,1592422,
 909         1585297,1578267,1571330,1564483,1557725,1551054,1544467,1537964,
 910         1531543,1525201,1518937,1512750,1506638,1500599,1494633,1488737,
 911         1482910,1477151,1471459,1465832,1460269,1454769,1449330,1443952,
 912         1438634,1433374,1428171,1423024,1417933,1412896,1407912,1402981,
 913         1398101,1393271,1388492,1383761,1379078,1374443,1369853,1365310,
 914         1360811,1356357,1351946,1347578,1343252,1338967,1334723,1330519,
 915         1326355,1322229,1318142,1314092,1310080,1306104,1302164,1298259,
 916         1294390,1290555,1286753,1282985,1279250,1275548,1271877,1268238,
 917         1264630,1261052,1257505,1253987,1250499,1247040,1243609,1240207,
 918         1236832,1233485,1230165,1226871,1223604,1220362,1217147,1213956,
 919         1210791,1207650,1204533,1201441,1198372,1195327,1192304,1189305,
 920         1186328,1183373,1180440,1177529,1174640,1171771,1168924,1166097,
 921         1163290,1160504,1157737,1154991,1152263,1149555,1146866,1144196,
 922         1141544,1138911,1136296,1133699,1131119,1128557,1126013,1123485,
 923         1120974,1118481,1116003,1113542,1111098,1108669,1106256,1103859,
 924         1101478,1099111,1096760,1094424,1092103,1089797,1087505,1085227,
 925         1082964,1080715,1078480,1076258,1074051,1071857,1069676,1067508,
 926         1065354,1063212,1061084,1058968,1056865,1054774,1052696,1050630,
 927         1048576,1046533,1044503,1042485,1040478,1038483,1036499,1034527,
 928         1032566,1030616,1028677,1026748,1024831,1022924,1021028,1019143,
 929         1017268,1015403,1013548,1011704,1009869,1008045,1006230,1004425,
 930         1002630,1000844,999068,997301,995544,993796,992057,990327,
 931         988606,986895,985192,983497,981812,980135,978467,976807,
 932         975155,973512,971878,970251,968633,967022,965420,963825,
 933         962239,960660,959089,957526,955970,954422,952881,951348,
 934         949822,948304,946793,945289,943792,942302,940819,939343,
 935         937874,936412,934957,933509,932067,930632,929204,927782,
 936         926366,924957,923555,922159,920769,919385,918008,916637,
 937         915272,913913,912560,911213,909872,908537,907207,905884,
 938         904566,903254,901948,900648,899353,898063,896779,895501,
 939         894228,892961,891698,890442,889190,887944,886703,885467,
 940         884236,883011,881790,880575,879365,878159,876959,875763,
 941         874572,873386,872205,871029,869858,868691,867529,866371,
 942         865218,864070,862926,861787,860653,859522,858397,857275,
 943         856158,855046,853937,852833,851734,850638,849547,848460,
 944         847377,846298,845223,844153,843086,842024,840965,839911,
 945         838860,837814,836771,835732,834697,833666,832639,831615,
 946         830595,829579,828567,827559,826554,825552,824555,823561,
 947         822570,821583,820600,819620,818644,817671,816702,815736,
 948         814773,813814,812858,811906,810957,810011,809069,808130,
 949         807194,806261,805332,804405,803482,802563,801646,800732,
 950         799822,798915,798010,797109,796211,795316,794424,793535,
 951         792648,791765,790885,790008,789133,788262,787393,786528,
 952         785665,784805,783947,783093,782241,781392,780546,779703,
 953         778862,778024,777189,776356,775527,774699,773875,773053,
 954         772233,771417,770603,769791,768982,768175,767371,766570,
 955         765771,764975,764181,763389,762600,761814,761029,760248,
 956         759468,758691,757917,757145,756375,755607,754842,754079,
 957         753319,752560,751805,751051,750299,749550,748803,748059,
 958         747316,746576,745838,745102,744368,743637,742907,742180,
 959         741455,740732,740011,739292,738575,737861,737148,736438,
 960         735729,735023,734318,733616,732916,732217,731521,730827,
 961         730134,729444,728755,728069,727384,726701,726021,725342,
 962         724665,723990,723317,722645,721976,721308,720643,719979,
 963         719317,718656,717998,717341,716687,716034,715382,714733,
 964         714085,713439,712795,712153,711512,710873,710236,709600,
 965         708966,708334,707704,707075,706448,705822,705198,704576,
 966         703956,703337,702720,702104,701490,700878,700267,699658,
 967         699050,698444,697840,697237,696635,696036,695437,694841,
 968         694246,693652,693060,692469,691880,691293,690707,690122,
 969         689539,688957,688377,687798,687221,686645,686071,685498,
 970         684926,684356,683788,683221,682655,682090,681527,680966,
 971         680405,679847,679289,678733,678178,677625,677073,676522,
 972         675973,675425,674878,674333,673789,673246,672705,672164,
 973         671626,671088,670552,670017,669483,668951,668420,667890,
 974         667361,666834,666308,665783,665259,664737,664216,663696,
 975         663177,662660,662143,661628,661114,660602,660090,659580,
 976         659071,658563,658056,657550,657046,656543,656041,655540,
 977         655040,654541,654043,653547,653052,652558,652065,651573,
 978         651082,650592,650103,649616,649129,648644,648160,647677,
 979         647195,646714,646234,645755,645277,644800,644325,643850,
 980         643376,642904,642432,641962,641492,641024,640557,640090,
 981         639625,639161,638697,638235,637774,637313,636854,636396,
 982         635938,635482,635026,634572,634119,633666,633215,632764,
 983         632315,631866,631418,630972,630526,630081,629637,629194,
 984         628752,628311,627871,627432,626993,626556,626120,625684,
 985         625249,624816,624383,623951,623520,623090,622660,622232,
 986         621804,621378,620952,620527,620103,619680,619258,618836,
 987         618416,617996,617577,617159,616742,616326,615910,615496,
 988         615082,614669,614257,613846,613435,613026,612617,612209,
 989         611802,611395,610990,610585,610181,609778,609375,608974,
 990         608573,608173,607774,607375,606978,606581,606185,605790,
 991         605395,605001,604608,604216,603825,603434,603044,602655,
 992         602266,601879,601492,601106,600720,600335,599952,599568,
 993         599186,598804,598423,598043,597663,597284,596906,596529,
 994         596152,595776,595401,595026,594652,594279,593907,593535,
 995         593164,592793,592424,592055,591686,591319,590952,590585,
 996         590220,589855,589491,589127,588764,588402,588041,587680,
 997         587320,586960,586601,586243,585885,585528,585172,584816,
 998         584462,584107,583754,583400,583048,582696,582345,581995,
 999         581645,581296,580947,580599,580252,579905,579559,579213,
1000         578868,578524,578181,577838,577495,577153,576812,576471,
1001         576131,575792,575453,575115,574777,574440,574104,573768,
1002         573433,573098,572764,572431,572098,571765,571434,571103,
1003         570772,570442,570113,569784,569455,569128,568800,568474,
1004         568148,567822,567497,567173,566849,566526,566203,565881,
1005         565559,565238,564918,564598,564278,563959,563641,563323,
1006         563006,562689,562373,562057,561742,561428,561114,560800,
1007         560487,560174,559862,559551,559240,558930,558620,558310,
1008         558001,557693,557385,557078,556771,556465,556159,555853,
1009         555549,555244,554940,554637,554334,554032,553730,553429,
1010         553128,552828,552528,552228,551929,551631,551333,551036,
1011         550739,550442,550146,549851,549555,549261,548967,548673,
1012         548380,548087,547795,547503,547212,546921,546631,546341,
1013         546051,545762,545474,545186,544898,544611,544324,544038,
1014         543752,543467,543182,542897,542613,542330,542047,541764,
1015         541482,541200,540919,540638,540357,540077,539798,539518,
1016         539240,538961,538683,538406,538129,537852,537576,537300,
1017         537025,536750,536476,536202,535928,535655,535382,535110,
1018         534838,534566,534295,534024,533754,533484,533214,532945,
1019         532677,532408,532140,531873,531606,531339,531073,530807,
1020         530542,530277,530012,529748,529484,529220,528957,528694,
1021         528432,528170,527909,527648,527387,527126,526866,526607,
1022         526348,526089,525830,525572,525315,525057,524800,524544
1023 };