maths/tables.c

   1 /* $Id: tables.c,v 1.5 2004-08-28 23:17:45 schaffner Exp $ */
   2 /*
   3 THE COMPUTER CODE CONTAINED HEREIN IS THE SOLE PROPERTY OF PARALLAX
   4 SOFTWARE CORPORATION ("PARALLAX").  PARALLAX, IN DISTRIBUTING THE CODE TO
   5 END-USERS, AND SUBJECT TO ALL OF THE TERMS AND CONDITIONS HEREIN, GRANTS A
   6 ROYALTY-FREE, PERPETUAL LICENSE TO SUCH END-USERS FOR USE BY SUCH END-USERS
   7 IN USING, DISPLAYING,  AND CREATING DERIVATIVE WORKS THEREOF, SO LONG AS
   8 SUCH USE, DISPLAY OR CREATION IS FOR NON-COMMERCIAL, ROYALTY OR REVENUE
   9 FREE PURPOSES.  IN NO EVENT SHALL THE END-USER USE THE COMPUTER CODE
  10 CONTAINED HEREIN FOR REVENUE-BEARING PURPOSES.  THE END-USER UNDERSTANDS
  11 AND AGREES TO THE TERMS HEREIN AND ACCEPTS THE SAME BY USE OF THIS FILE.
  12 COPYRIGHT 1993-1998 PARALLAX SOFTWARE CORPORATION.  ALL RIGHTS RESERVED.
  13 */
  14
  15 /*
  16  *
  17  * C version of fixed point library
  18  *
  19  */
  20
  21 #ifdef HAVE_CONFIG_H
  22 #include <conf.h>
  23 #endif
  24
  25 #include "maths.h"
  26
  27 ubyte guess_table[] = {
  28         1,
  29         1,1,1,
  30         2,2,2,2,2,
  31         3,3,3,3,3,3,3,
  32         4,4,4,4,4,4,4,4,4,
  33         5,5,5,5,5,5,5,5,5,5,5,
  34         6,6,6,6,6,6,6,6,6,6,6,6,6,
  35         7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
  36         8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
  37         9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
  38         10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
  39         11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
  40         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,
  41         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,
  42         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,
  43         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
  44 };
  45
  46 short sincos_table[] = {
  47         0,
  48         402,
  49         804,
  50         1205,
  51         1606,
  52         2006,
  53         2404,
  54         2801,
  55         3196,
  56         3590,
  57         3981,
  58         4370,
  59         4756,
  60         5139,
  61         5520,
  62         5897,
  63         6270,
  64         6639,
  65         7005,
  66         7366,
  67         7723,
  68         8076,
  69         8423,
  70         8765,
  71         9102,
  72         9434,
  73         9760,
  74         10080,
  75         10394,
  76         10702,
  77         11003,
  78         11297,
  79         11585,
  80         11866,
  81         12140,
  82         12406,
  83         12665,
  84         12916,
  85         13160,
  86         13395,
  87         13623,
  88         13842,
  89         14053,
  90         14256,
  91         14449,
  92         14635,
  93         14811,
  94         14978,
  95         15137,
  96         15286,
  97         15426,
  98         15557,
  99         15679,
 100         15791,
 101         15893,
 102         15986,
 103         16069,
 104         16143,
 105         16207,
 106         16261,
 107         16305,
 108         16340,
 109         16364,
 110         16379,
 111         // cos_table
 112         16384,
 113         16379,
 114         16364,
 115         16340,
 116         16305,
 117         16261,
 118         16207,
 119         16143,
 120         16069,
 121         15986,
 122         15893,
 123         15791,
 124         15679,
 125         15557,
 126         15426,
 127         15286,
 128         15137,
 129         14978,
 130         14811,
 131         14635,
 132         14449,
 133         14256,
 134         14053,
 135         13842,
 136         13623,
 137         13395,
 138         13160,
 139         12916,
 140         12665,
 141         12406,
 142         12140,
 143         11866,
 144         11585,
 145         11297,
 146         11003,
 147         10702,
 148         10394,
 149         10080,
 150         9760,
 151         9434,
 152         9102,
 153         8765,
 154         8423,
 155         8076,
 156         7723,
 157         7366,
 158         7005,
 159         6639,
 160         6270,
 161         5897,
 162         5520,
 163         5139,
 164         4756,
 165         4370,
 166         3981,
 167         3590,
 168         3196,
 169         2801,
 170         2404,
 171         2006,
 172         1606,
 173         1205,
 174         804,
 175         402,
 176         0,
 177         -402,
 178         -804,
 179         -1205,
 180         -1606,
 181         -2006,
 182         -2404,
 183         -2801,
 184         -3196,
 185         -3590,
 186         -3981,
 187         -4370,
 188         -4756,
 189         -5139,
 190         -5520,
 191         -5897,
 192         -6270,
 193         -6639,
 194         -7005,
 195         -7366,
 196         -7723,
 197         -8076,
 198         -8423,
 199         -8765,
 200         -9102,
 201         -9434,
 202         -9760,
 203         -10080,
 204         -10394,
 205         -10702,
 206         -11003,
 207         -11297,
 208         -11585,
 209         -11866,
 210         -12140,
 211         -12406,
 212         -12665,
 213         -12916,
 214         -13160,
 215         -13395,
 216         -13623,
 217         -13842,
 218         -14053,
 219         -14256,
 220         -14449,
 221         -14635,
 222         -14811,
 223         -14978,
 224         -15137,
 225         -15286,
 226         -15426,
 227         -15557,
 228         -15679,
 229         -15791,
 230         -15893,
 231         -15986,
 232         -16069,
 233         -16143,
 234         -16207,
 235         -16261,
 236         -16305,
 237         -16340,
 238         -16364,
 239         -16379,
 240         -16384,
 241         -16379,
 242         -16364,
 243         -16340,
 244         -16305,
 245         -16261,
 246         -16207,
 247         -16143,
 248         -16069,
 249         -15986,
 250         -15893,
 251         -15791,
 252         -15679,
 253         -15557,
 254         -15426,
 255         -15286,
 256         -15137,
 257         -14978,
 258         -14811,
 259         -14635,
 260         -14449,
 261         -14256,
 262         -14053,
 263         -13842,
 264         -13623,
 265         -13395,
 266         -13160,
 267         -12916,
 268         -12665,
 269         -12406,
 270         -12140,
 271         -11866,
 272         -11585,
 273         -11297,
 274         -11003,
 275         -10702,
 276         -10394,
 277         -10080,
 278         -9760,
 279         -9434,
 280         -9102,
 281         -8765,
 282         -8423,
 283         -8076,
 284         -7723,
 285         -7366,
 286         -7005,
 287         -6639,
 288         -6270,
 289         -5897,
 290         -5520,
 291         -5139,
 292         -4756,
 293         -4370,
 294         -3981,
 295         -3590,
 296         -3196,
 297         -2801,
 298         -2404,
 299         -2006,
 300         -1606,
 301         -1205,
 302         -804,
 303         -402,
 304         0,
 305         402,
 306         804,
 307         1205,
 308         1606,
 309         2006,
 310         2404,
 311         2801,
 312         3196,
 313         3590,
 314         3981,
 315         4370,
 316         4756,
 317         5139,
 318         5520,
 319         5897,
 320         6270,
 321         6639,
 322         7005,
 323         7366,
 324         7723,
 325         8076,
 326         8423,
 327         8765,
 328         9102,
 329         9434,
 330         9760,
 331         10080,
 332         10394,
 333         10702,
 334         11003,
 335         11297,
 336         11585,
 337         11866,
 338         12140,
 339         12406,
 340         12665,
 341         12916,
 342         13160,
 343         13395,
 344         13623,
 345         13842,
 346         14053,
 347         14256,
 348         14449,
 349         14635,
 350         14811,
 351         14978,
 352         15137,
 353         15286,
 354         15426,
 355         15557,
 356         15679,
 357         15791,
 358         15893,
 359         15986,
 360         16069,
 361         16143,
 362         16207,
 363         16261,
 364         16305,
 365         16340,
 366         16364,
 367         16379,
 368         16384
 369 };
 370
 371 ushort asin_table[] = {
 372         0,
 373         41,
 374         81,
 375         122,
 376         163,
 377         204,
 378         244,
 379         285,
 380         326,
 381         367,
 382         408,
 383         448,
 384         489,
 385         530,
 386         571,
 387         612,
 388         652,
 389         693,
 390         734,
 391         775,
 392         816,
 393         857,
 394         897,
 395         938,
 396         979,
 397         1020,
 398         1061,
 399         1102,
 400         1143,
 401         1184,
 402         1225,
 403         1266,
 404         1307,
 405         1348,
 406         1389,
 407         1431,
 408         1472,
 409         1513,
 410         1554,
 411         1595,
 412         1636,
 413         1678,
 414         1719,
 415         1760,
 416         1802,
 417         1843,
 418         1884,
 419         1926,
 420         1967,
 421         2009,
 422         2050,
 423         2092,
 424         2134,
 425         2175,
 426         2217,
 427         2259,
 428         2300,
 429         2342,
 430         2384,
 431         2426,
 432         2468,
 433         2510,
 434         2551,
 435         2593,
 436         2636,
 437         2678,
 438         2720,
 439         2762,
 440         2804,
 441         2847,
 442         2889,
 443         2931,
 444         2974,
 445         3016,
 446         3059,
 447         3101,
 448         3144,
 449         3187,
 450         3229,
 451         3272,
 452         3315,
 453         3358,
 454         3401,
 455         3444,
 456         3487,
 457         3530,
 458         3573,
 459         3617,
 460         3660,
 461         3704,
 462         3747,
 463         3791,
 464         3834,
 465         3878,
 466         3922,
 467         3965,
 468         4009,
 469         4053,
 470         4097,
 471         4142,
 472         4186,
 473         4230,
 474         4275,
 475         4319,
 476         4364,
 477         4408,
 478         4453,
 479         4498,
 480         4543,
 481         4588,
 482         4633,
 483         4678,
 484         4723,
 485         4768,
 486         4814,
 487         4859,
 488         4905,
 489         4951,
 490         4997,
 491         5043,
 492         5089,
 493         5135,
 494         5181,
 495         5228,
 496         5274,
 497         5321,
 498         5367,
 499         5414,
 500         5461,
 501         5508,
 502         5556,
 503         5603,
 504         5651,
 505         5698,
 506         5746,
 507         5794,
 508         5842,
 509         5890,
 510         5938,
 511         5987,
 512         6035,
 513         6084,
 514         6133,
 515         6182,
 516         6231,
 517         6281,
 518         6330,
 519         6380,
 520         6430,
 521         6480,
 522         6530,
 523         6580,
 524         6631,
 525         6681,
 526         6732,
 527         6783,
 528         6835,
 529         6886,
 530         6938,
 531         6990,
 532         7042,
 533         7094,
 534         7147,
 535         7199,
 536         7252,
 537         7306,
 538         7359,
 539         7413,
 540         7466,
 541         7521,
 542         7575,
 543         7630,
 544         7684,
 545         7740,
 546         7795,
 547         7851,
 548         7907,
 549         7963,
 550         8019,
 551         8076,
 552         8133,
 553         8191,
 554         8249,
 555         8307,
 556         8365,
 557         8424,
 558         8483,
 559         8543,
 560         8602,
 561         8663,
 562         8723,
 563         8784,
 564         8846,
 565         8907,
 566         8970,
 567         9032,
 568         9095,
 569         9159,
 570         9223,
 571         9288,
 572         9353,
 573         9418,
 574         9484,
 575         9551,
 576         9618,
 577         9686,
 578         9754,
 579         9823,
 580         9892,
 581         9963,
 582         10034,
 583         10105,
 584         10177,
 585         10251,
 586         10324,
 587         10399,
 588         10475,
 589         10551,
 590         10628,
 591         10706,
 592         10785,
 593         10866,
 594         10947,
 595         11029,
 596         11113,
 597         11198,
 598         11284,
 599         11371,
 600         11460,
 601         11550,
 602         11642,
 603         11736,
 604         11831,
 605         11929,
 606         12028,
 607         12130,
 608         12234,
 609         12340,
 610         12449,
 611         12561,
 612         12677,
 613         12796,
 614         12919,
 615         13046,
 616         13178,
 617         13315,
 618         13459,
 619         13610,
 620         13770,
 621         13939,
 622         14121,
 623         14319,
 624         14538,
 625         14786,
 626         15079,
 627         15462,
 628         16384,
 629         16384   // extra for when exactly 1
 630 };
 631
 632 ushort acos_table[] = {
 633         16384,
 634         16343,
 635         16303,
 636         16262,
 637         16221,
 638         16180,
 639         16140,
 640         16099,
 641         16058,
 642         16017,
 643         15976,
 644         15936,
 645         15895,
 646         15854,
 647         15813,
 648         15772,
 649         15732,
 650         15691,
 651         15650,
 652         15609,
 653         15568,
 654         15527,
 655         15487,
 656         15446,
 657         15405,
 658         15364,
 659         15323,
 660         15282,
 661         15241,
 662         15200,
 663         15159,
 664         15118,
 665         15077,
 666         15036,
 667         14995,
 668         14953,
 669         14912,
 670         14871,
 671         14830,
 672         14789,
 673         14748,
 674         14706,
 675         14665,
 676         14624,
 677         14582,
 678         14541,
 679         14500,
 680         14458,
 681         14417,
 682         14375,
 683         14334,
 684         14292,
 685         14250,
 686         14209,
 687         14167,
 688         14125,
 689         14084,
 690         14042,
 691         14000,
 692         13958,
 693         13916,
 694         13874,
 695         13833,
 696         13791,
 697         13748,
 698         13706,
 699         13664,
 700         13622,
 701         13580,
 702         13537,
 703         13495,
 704         13453,
 705         13410,
 706         13368,
 707         13325,
 708         13283,
 709         13240,
 710         13197,
 711         13155,
 712         13112,
 713         13069,
 714         13026,
 715         12983,
 716         12940,
 717         12897,
 718         12854,
 719         12811,
 720         12767,
 721         12724,
 722         12680,
 723         12637,
 724         12593,
 725         12550,
 726         12506,
 727         12462,
 728         12419,
 729         12375,
 730         12331,
 731         12287,
 732         12242,
 733         12198,
 734         12154,
 735         12109,
 736         12065,
 737         12020,
 738         11976,
 739         11931,
 740         11886,
 741         11841,
 742         11796,
 743         11751,
 744         11706,
 745         11661,
 746         11616,
 747         11570,
 748         11525,
 749         11479,
 750         11433,
 751         11387,
 752         11341,
 753         11295,
 754         11249,
 755         11203,
 756         11156,
 757         11110,
 758         11063,
 759         11017,
 760         10970,
 761         10923,
 762         10876,
 763         10828,
 764         10781,
 765         10733,
 766         10686,
 767         10638,
 768         10590,
 769         10542,
 770         10494,
 771         10446,
 772         10397,
 773         10349,
 774         10300,
 775         10251,
 776         10202,
 777         10153,
 778         10103,
 779         10054,
 780         10004,
 781         9954,
 782         9904,
 783         9854,
 784         9804,
 785         9753,
 786         9703,
 787         9652,
 788         9601,
 789         9549,
 790         9498,
 791         9446,
 792         9394,
 793         9342,
 794         9290,
 795         9237,
 796         9185,
 797         9132,
 798         9078,
 799         9025,
 800         8971,
 801         8918,
 802         8863,
 803         8809,
 804         8754,
 805         8700,
 806         8644,
 807         8589,
 808         8533,
 809         8477,
 810         8421,
 811         8365,
 812         8308,
 813         8251,
 814         8193,
 815         8135,
 816         8077,
 817         8019,
 818         7960,
 819         7901,
 820         7841,
 821         7782,
 822         7721,
 823         7661,
 824         7600,
 825         7538,
 826         7477,
 827         7414,
 828         7352,
 829         7289,
 830         7225,
 831         7161,
 832         7096,
 833         7031,
 834         6966,
 835         6900,
 836         6833,
 837         6766,
 838         6698,
 839         6630,
 840         6561,
 841         6492,
 842         6421,
 843         6350,
 844         6279,
 845         6207,
 846         6133,
 847         6060,
 848         5985,
 849         5909,
 850         5833,
 851         5756,
 852         5678,
 853         5599,
 854         5518,
 855         5437,
 856         5355,
 857         5271,
 858         5186,
 859         5100,
 860         5013,
 861         4924,
 862         4834,
 863         4742,
 864         4648,
 865         4553,
 866         4455,
 867         4356,
 868         4254,
 869         4150,
 870         4044,
 871         3935,
 872         3823,
 873         3707,
 874         3588,
 875         3465,
 876         3338,
 877         3206,
 878         3069,
 879         2925,
 880         2774,
 881         2614,
 882         2445,
 883         2263,
 884         2065,
 885         1846,
 886         1598,
 887         1305,
 888         922,
 889         0,
 890         0   // extra for when exactly 1
 891 };
 892
 893 fix isqrt_guess_table[] = {
 894         // 0,
 895         0x80000000,
 896         16777216,11863283,9686330,8388608,7502999,6849269,6341191,
 897         5931641,5592405,5305421,5058520,4843165,4653162,4483899,4331858,
 898         4194304,4069072,3954427,3848957,3751499,3661088,3576914,3498291,
 899         3424634,3355443,3290282,3228776,3170595,3115450,3063086,3013276,
 900         2965820,2920538,2877268,2835867,2796202,2758157,2721623,2686504,
 901         2652710,2620160,2588780,2558501,2529260,2500999,2473665,2447208,
 902         2421582,2396745,2372656,2349280,2326581,2304527,2283089,2262239,
 903         2241949,2222196,2202956,2184207,2165929,2148102,2130708,2113730,
 904         2097152,2080957,2065132,2049663,2034536,2019739,2005260,1991089,
 905         1977213,1963624,1950311,1937266,1924478,1911941,1899645,1887584,
 906         1875749,1864135,1852733,1841538,1830544,1819744,1809133,1798706,
 907         1788457,1778381,1768473,1758730,1749145,1739716,1730437,1721306,
 908         1712317,1703468,1694754,1686173,1677721,1669395,1661191,1653108,
 909         1645141,1637288,1629547,1621914,1614388,1606965,1599644,1592422,
 910         1585297,1578267,1571330,1564483,1557725,1551054,1544467,1537964,
 911         1531543,1525201,1518937,1512750,1506638,1500599,1494633,1488737,
 912         1482910,1477151,1471459,1465832,1460269,1454769,1449330,1443952,
 913         1438634,1433374,1428171,1423024,1417933,1412896,1407912,1402981,
 914         1398101,1393271,1388492,1383761,1379078,1374443,1369853,1365310,
 915         1360811,1356357,1351946,1347578,1343252,1338967,1334723,1330519,
 916         1326355,1322229,1318142,1314092,1310080,1306104,1302164,1298259,
 917         1294390,1290555,1286753,1282985,1279250,1275548,1271877,1268238,
 918         1264630,1261052,1257505,1253987,1250499,1247040,1243609,1240207,
 919         1236832,1233485,1230165,1226871,1223604,1220362,1217147,1213956,
 920         1210791,1207650,1204533,1201441,1198372,1195327,1192304,1189305,
 921         1186328,1183373,1180440,1177529,1174640,1171771,1168924,1166097,
 922         1163290,1160504,1157737,1154991,1152263,1149555,1146866,1144196,
 923         1141544,1138911,1136296,1133699,1131119,1128557,1126013,1123485,
 924         1120974,1118481,1116003,1113542,1111098,1108669,1106256,1103859,
 925         1101478,1099111,1096760,1094424,1092103,1089797,1087505,1085227,
 926         1082964,1080715,1078480,1076258,1074051,1071857,1069676,1067508,
 927         1065354,1063212,1061084,1058968,1056865,1054774,1052696,1050630,
 928         1048576,1046533,1044503,1042485,1040478,1038483,1036499,1034527,
 929         1032566,1030616,1028677,1026748,1024831,1022924,1021028,1019143,
 930         1017268,1015403,1013548,1011704,1009869,1008045,1006230,1004425,
 931         1002630,1000844,999068,997301,995544,993796,992057,990327,
 932         988606,986895,985192,983497,981812,980135,978467,976807,
 933         975155,973512,971878,970251,968633,967022,965420,963825,
 934         962239,960660,959089,957526,955970,954422,952881,951348,
 935         949822,948304,946793,945289,943792,942302,940819,939343,
 936         937874,936412,934957,933509,932067,930632,929204,927782,
 937         926366,924957,923555,922159,920769,919385,918008,916637,
 938         915272,913913,912560,911213,909872,908537,907207,905884,
 939         904566,903254,901948,900648,899353,898063,896779,895501,
 940         894228,892961,891698,890442,889190,887944,886703,885467,
 941         884236,883011,881790,880575,879365,878159,876959,875763,
 942         874572,873386,872205,871029,869858,868691,867529,866371,
 943         865218,864070,862926,861787,860653,859522,858397,857275,
 944         856158,855046,853937,852833,851734,850638,849547,848460,
 945         847377,846298,845223,844153,843086,842024,840965,839911,
 946         838860,837814,836771,835732,834697,833666,832639,831615,
 947         830595,829579,828567,827559,826554,825552,824555,823561,
 948         822570,821583,820600,819620,818644,817671,816702,815736,
 949         814773,813814,812858,811906,810957,810011,809069,808130,
 950         807194,806261,805332,804405,803482,802563,801646,800732,
 951         799822,798915,798010,797109,796211,795316,794424,793535,
 952         792648,791765,790885,790008,789133,788262,787393,786528,
 953         785665,784805,783947,783093,782241,781392,780546,779703,
 954         778862,778024,777189,776356,775527,774699,773875,773053,
 955         772233,771417,770603,769791,768982,768175,767371,766570,
 956         765771,764975,764181,763389,762600,761814,761029,760248,
 957         759468,758691,757917,757145,756375,755607,754842,754079,
 958         753319,752560,751805,751051,750299,749550,748803,748059,
 959         747316,746576,745838,745102,744368,743637,742907,742180,
 960         741455,740732,740011,739292,738575,737861,737148,736438,
 961         735729,735023,734318,733616,732916,732217,731521,730827,
 962         730134,729444,728755,728069,727384,726701,726021,725342,
 963         724665,723990,723317,722645,721976,721308,720643,719979,
 964         719317,718656,717998,717341,716687,716034,715382,714733,
 965         714085,713439,712795,712153,711512,710873,710236,709600,
 966         708966,708334,707704,707075,706448,705822,705198,704576,
 967         703956,703337,702720,702104,701490,700878,700267,699658,
 968         699050,698444,697840,697237,696635,696036,695437,694841,
 969         694246,693652,693060,692469,691880,691293,690707,690122,
 970         689539,688957,688377,687798,687221,686645,686071,685498,
 971         684926,684356,683788,683221,682655,682090,681527,680966,
 972         680405,679847,679289,678733,678178,677625,677073,676522,
 973         675973,675425,674878,674333,673789,673246,672705,672164,
 974         671626,671088,670552,670017,669483,668951,668420,667890,
 975         667361,666834,666308,665783,665259,664737,664216,663696,
 976         663177,662660,662143,661628,661114,660602,660090,659580,
 977         659071,658563,658056,657550,657046,656543,656041,655540,
 978         655040,654541,654043,653547,653052,652558,652065,651573,
 979         651082,650592,650103,649616,649129,648644,648160,647677,
 980         647195,646714,646234,645755,645277,644800,644325,643850,
 981         643376,642904,642432,641962,641492,641024,640557,640090,
 982         639625,639161,638697,638235,637774,637313,636854,636396,
 983         635938,635482,635026,634572,634119,633666,633215,632764,
 984         632315,631866,631418,630972,630526,630081,629637,629194,
 985         628752,628311,627871,627432,626993,626556,626120,625684,
 986         625249,624816,624383,623951,623520,623090,622660,622232,
 987         621804,621378,620952,620527,620103,619680,619258,618836,
 988         618416,617996,617577,617159,616742,616326,615910,615496,
 989         615082,614669,614257,613846,613435,613026,612617,612209,
 990         611802,611395,610990,610585,610181,609778,609375,608974,
 991         608573,608173,607774,607375,606978,606581,606185,605790,
 992         605395,605001,604608,604216,603825,603434,603044,602655,
 993         602266,601879,601492,601106,600720,600335,599952,599568,
 994         599186,598804,598423,598043,597663,597284,596906,596529,
 995         596152,595776,595401,595026,594652,594279,593907,593535,
 996         593164,592793,592424,592055,591686,591319,590952,590585,
 997         590220,589855,589491,589127,588764,588402,588041,587680,
 998         587320,586960,586601,586243,585885,585528,585172,584816,
 999         584462,584107,583754,583400,583048,582696,582345,581995,
1000         581645,581296,580947,580599,580252,579905,579559,579213,
1001         578868,578524,578181,577838,577495,577153,576812,576471,
1002         576131,575792,575453,575115,574777,574440,574104,573768,
1003         573433,573098,572764,572431,572098,571765,571434,571103,
1004         570772,570442,570113,569784,569455,569128,568800,568474,
1005         568148,567822,567497,567173,566849,566526,566203,565881,
1006         565559,565238,564918,564598,564278,563959,563641,563323,
1007         563006,562689,562373,562057,561742,561428,561114,560800,
1008         560487,560174,559862,559551,559240,558930,558620,558310,
1009         558001,557693,557385,557078,556771,556465,556159,555853,
1010         555549,555244,554940,554637,554334,554032,553730,553429,
1011         553128,552828,552528,552228,551929,551631,551333,551036,
1012         550739,550442,550146,549851,549555,549261,548967,548673,
1013         548380,548087,547795,547503,547212,546921,546631,546341,
1014         546051,545762,545474,545186,544898,544611,544324,544038,
1015         543752,543467,543182,542897,542613,542330,542047,541764,
1016         541482,541200,540919,540638,540357,540077,539798,539518,
1017         539240,538961,538683,538406,538129,537852,537576,537300,
1018         537025,536750,536476,536202,535928,535655,535382,535110,
1019         534838,534566,534295,534024,533754,533484,533214,532945,
1020         532677,532408,532140,531873,531606,531339,531073,530807,
1021         530542,530277,530012,529748,529484,529220,528957,528694,
1022         528432,528170,527909,527648,527387,527126,526866,526607,
1023         526348,526089,525830,525572,525315,525057,524800,524544
1024 };