/***************************************************************************  **************************************************************************                  Spherical Harmonic Transform Kit 2.7       Contact: Peter Kostelec            geelong@cs.dartmouth.edu       Copyright 1997-2003  Sean Moore, Dennis Healy,                        Dan Rockmore, Peter Kostelec       Copyright 2004  Peter Kostelec, Dan Rockmore     SpharmonicKit is free software; you can redistribute it and/or modify     it under the terms of the GNU General Public License as published by     the Free Software Foundation; either version 2 of the License, or     (at your option) any later version.       SpharmonicKit is distributed in the hope that it will be useful,     but WITHOUT ANY WARRANTY; without even the implied warranty of     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the     GNU General Public License for more details.       You should have received a copy of the GNU General Public License     along with this program; if not, write to the Free Software     Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.       Commercial use is absolutely prohibited.     See the accompanying LICENSE file for details.    ************************************************************************  ************************************************************************//****  OUR permutations: permutation arrays used in FCTs. See Sean's  thesis for details. The interface function (defined at the  bottom of this file) is  const int *get_perm(int n)  ****/static const int OUR4[4] = {0, 3, 2, 1};static const int OUR8[8] = {0, 7, 4, 3, 2, 5, 6, 1};static const int OUR16[16] ={0, 15, 8, 7, 4, 11, 12, 3, 2, 13, 10, 5, 6, 9, 14, 1};static const int OUR32[32] = {0, 31, 16, 15, 8, 23, 24, 7, 4, 27, 20, 11, 12, 19, 28, 3, 2, 29, 18, 13,   10, 21, 26, 5, 6, 25, 22, 9, 14, 17, 30, 1};static const int OUR64[64] = {0, 63, 32, 31, 16, 47, 48, 15, 8, 55, 40, 23, 24, 39, 56, 7, 4, 59, 36, 27,   20, 43, 52, 11, 12, 51, 44, 19, 28, 35, 60, 3, 2, 61, 34, 29, 18, 45, 50,   13, 10, 53, 42, 21, 26, 37, 58, 5, 6, 57, 38, 25, 22, 41, 54, 9, 14, 49,   46, 17, 30, 33, 62, 1};static const int OUR128[128] = {0, 127, 64, 63, 32, 95, 96, 31, 16, 111, 80, 47, 48, 79, 112, 15, 8, 119,   72, 55, 40, 87, 104, 23, 24, 103, 88, 39, 56, 71, 120, 7, 4, 123, 68, 59,   36, 91, 100, 27, 20, 107, 84, 43, 52, 75, 116, 11, 12, 115, 76, 51, 44, 83,   108, 19, 28, 99, 92, 35, 60, 67, 124, 3, 2, 125, 66, 61, 34, 93, 98, 29,   18, 109, 82, 45, 50, 77, 114, 13, 10, 117, 74, 53, 42, 85, 106, 21, 26,   101, 90, 37, 58, 69, 122, 5, 6, 121, 70, 57, 38, 89, 102, 25, 22, 105, 86,   41, 54, 73, 118, 9, 14, 113, 78, 49, 46, 81, 110, 17, 30, 97, 94, 33, 62,   65, 126, 1};static const int OUR256[256] = {0, 255, 128, 127, 64, 191, 192, 63, 32, 223, 160, 95, 96, 159, 224, 31, 16,   239, 144, 111, 80, 175, 208, 47, 48, 207, 176, 79, 112, 143, 240, 15, 8,   247, 136, 119, 72, 183, 200, 55, 40, 215, 168, 87, 104, 151, 232, 23, 24,   231, 152, 103, 88, 167, 216, 39, 56, 199, 184, 71, 120, 135, 248, 7, 4,   251, 132, 123, 68, 187, 196, 59, 36, 219, 164, 91, 100, 155, 228, 27, 20,   235, 148, 107, 84, 171, 212, 43, 52, 203, 180, 75, 116, 139, 244, 11, 12,   243, 140, 115, 76, 179, 204, 51, 44, 211, 172, 83, 108, 147, 236, 19, 28,   227, 156, 99, 92, 163, 220, 35, 60, 195, 188, 67, 124, 131, 252, 3, 2, 253,   130, 125, 66, 189, 194, 61, 34, 221, 162, 93, 98, 157, 226, 29, 18, 237,   146, 109, 82, 173, 210, 45, 50, 205, 178, 77, 114, 141, 242, 13, 10, 245,   138, 117, 74, 181, 202, 53, 42, 213, 170, 85, 106, 149, 234, 21, 26, 229,   154, 101, 90, 165, 218, 37, 58, 197, 186, 69, 122, 133, 250, 5, 6, 249,   134, 121, 70, 185, 198, 57, 38, 217, 166, 89, 102, 153, 230, 25, 22, 233,   150, 105, 86, 169, 214, 41, 54, 201, 182, 73, 118, 137, 246, 9, 14, 241,   142, 113, 78, 177, 206, 49, 46, 209, 174, 81, 110, 145, 238, 17, 30, 225,   158, 97, 94, 161, 222, 33, 62, 193, 190, 65, 126, 129, 254, 1};static const int OUR512[512] = {0, 511, 256, 255, 128, 383, 384, 127, 64, 447, 320, 191, 192, 319, 448, 63,   32, 479, 288, 223, 160, 351, 416, 95, 96, 415, 352, 159, 224, 287, 480, 31,   16, 495, 272, 239, 144, 367, 400, 111, 80, 431, 336, 175, 208, 303, 464,   47, 48, 463, 304, 207, 176, 335, 432, 79, 112, 399, 368, 143, 240, 271,   496, 15, 8, 503, 264, 247, 136, 375, 392, 119, 72, 439, 328, 183, 200, 311,   456, 55, 40, 471, 296, 215, 168, 343, 424, 87, 104, 407, 360, 151, 232,   279, 488, 23, 24, 487, 280, 231, 152, 359, 408, 103, 88, 423, 344, 167,   216, 295, 472, 39, 56, 455, 312, 199, 184, 327, 440, 71, 120, 391, 376,   135, 248, 263, 504, 7, 4, 507, 260, 251, 132, 379, 388, 123, 68, 443, 324,   187, 196, 315, 452, 59, 36, 475, 292, 219, 164, 347, 420, 91, 100, 411,   356, 155, 228, 283, 484, 27, 20, 491, 276, 235, 148, 363, 404, 107, 84,   427, 340, 171, 212, 299, 468, 43, 52, 459, 308, 203, 180, 331, 436, 75,   116, 395, 372, 139, 244, 267, 500, 11, 12, 499, 268, 243, 140, 371, 396,   115, 76, 435, 332, 179, 204, 307, 460, 51, 44, 467, 300, 211, 172, 339,   428, 83, 108, 403, 364, 147, 236, 275, 492, 19, 28, 483, 284, 227, 156,   355, 412, 99, 92, 419, 348, 163, 220, 291, 476, 35, 60, 451, 316, 195, 188,   323, 444, 67, 124, 387, 380, 131, 252, 259, 508, 3, 2, 509, 258, 253, 130,   381, 386, 125, 66, 445, 322, 189, 194, 317, 450, 61, 34, 477, 290, 221,   162, 349, 418, 93, 98, 413, 354, 157, 226, 285, 482, 29, 18, 493, 274, 237,   146, 365, 402, 109, 82, 429, 338, 173, 210, 301, 466, 45, 50, 461, 306,   205, 178, 333, 434, 77, 114, 397, 370, 141, 242, 269, 498, 13, 10, 501,   266, 245, 138, 373, 394, 117, 74, 437, 330, 181, 202, 309, 458, 53, 42,   469, 298, 213, 170, 341, 426, 85, 106, 405, 362, 149, 234, 277, 490, 21,   26, 485, 282, 229, 154, 357, 410, 101, 90, 421, 346, 165, 218, 293, 474,   37, 58, 453, 314, 197, 186, 325, 442, 69, 122, 389, 378, 133, 250, 261,   506, 5, 6, 505, 262, 249, 134, 377, 390, 121, 70, 441, 326, 185, 198, 313,   454, 57, 38, 473, 294, 217, 166, 345, 422, 89, 102, 409, 358, 153, 230,   281, 486, 25, 22, 489, 278, 233, 150, 361, 406, 105, 86, 425, 342, 169,   214, 297, 470, 41, 54, 457, 310, 201, 182, 329, 438, 73, 118, 393, 374,   137, 246, 265, 502, 9, 14, 497, 270, 241, 142, 369, 398, 113, 78, 433, 334,   177, 206, 305, 462, 49, 46, 465, 302, 209, 174, 337, 430, 81, 110, 401,   366, 145, 238, 273, 494, 17, 30, 481, 286, 225, 158, 353, 414, 97, 94, 417,   350, 161, 222, 289, 478, 33, 62, 449, 318, 193, 190, 321, 446, 65, 126,   385, 382, 129, 254, 257, 510, 1};static const int OUR1024[1024] = {0, 1023, 512, 511, 256, 767, 768, 255, 128, 895, 640, 383, 384, 639, 896,   127, 64, 959, 576, 447, 320, 703, 832, 191, 192, 831, 704, 319, 448, 575,   960, 63, 32, 991, 544, 479, 288, 735, 800, 223, 160, 863, 672, 351, 416,   607, 928, 95, 96, 927, 608, 415, 352, 671, 864, 159, 224, 799, 736, 287,   480, 543, 992, 31, 16, 1007, 528, 495, 272, 751, 784, 239, 144, 879, 656,   367, 400, 623, 912, 111, 80, 943, 592, 431, 336, 687, 848, 175, 208, 815,   720, 303, 464, 559, 976, 47, 48, 975, 560, 463, 304, 719, 816, 207, 176,   847, 688, 335, 432, 591, 944, 79, 112, 911, 624, 399, 368, 655, 880, 143,   240, 783, 752, 271, 496, 527, 1008, 15, 8, 1015, 520, 503, 264, 759, 776,   247, 136, 887, 648, 375, 392, 631, 904, 119, 72, 951, 584, 439, 328, 695,   840, 183, 200, 823, 712, 311, 456, 567, 968, 55, 40, 983, 552, 471, 296,   727, 808, 215, 168, 855, 680, 343, 424, 599, 936, 87, 104, 919, 616, 407,   360, 663, 872, 151, 232, 791, 744, 279, 488, 535, 1000, 23, 24, 999, 536,   487, 280, 743, 792, 231, 152, 871, 664, 359, 408, 615, 920, 103, 88, 935,   600, 423, 344, 679, 856, 167, 216, 807, 728, 295, 472, 551, 984, 39, 56,   967, 568, 455, 312, 711, 824, 199, 184, 839, 696, 327, 440, 583, 952, 71,   120, 903, 632, 391, 376, 647, 888, 135, 248, 775, 760, 263, 504, 519, 1016,   7, 4, 1019, 516, 507, 260, 763, 772, 251, 132, 891, 644, 379, 388, 635,   900, 123, 68, 955, 580, 443, 324, 699, 836, 187, 196, 827, 708, 315, 452,   571, 964, 59, 36, 987, 548, 475, 292, 731, 804, 219, 164, 859, 676, 347,   420, 603, 932, 91, 100, 923, 612, 411, 356, 667, 868, 155, 228, 795, 740,   283, 484, 539, 996, 27, 20, 1003, 532, 491, 276, 747, 788, 235, 148, 875,   660, 363, 404, 619, 916, 107, 84, 939, 596, 427, 340, 683, 852, 171, 212,   811, 724, 299, 468, 555, 980, 43, 52, 971, 564, 459, 308, 715, 820, 203,   180, 843, 692, 331, 436, 587, 948, 75, 116, 907, 628, 395, 372, 651, 884,   139, 244, 779, 756, 267, 500, 523, 1012, 11, 12, 1011, 524, 499, 268, 755,   780, 243, 140, 883, 652, 371, 396, 627, 908, 115, 76, 947, 588, 435, 332,   691, 844, 179, 204, 819, 716, 307, 460, 563, 972, 51, 44, 979, 556, 467,   300, 723, 812, 211, 172, 851, 684, 339, 428, 595, 940, 83, 108, 915, 620,   403, 364, 659, 876, 147, 236, 787, 748, 275, 492, 531, 1004, 19, 28, 995,   540, 483, 284, 739, 796, 227, 156, 867, 668, 355, 412, 611, 924, 99, 92,   931, 604, 419, 348, 675, 860, 163, 220, 803, 732, 291, 476, 547, 988, 35,   60, 963, 572, 451, 316, 707, 828, 195, 188, 835, 700, 323, 444, 579, 956,   67, 124, 899, 636, 387, 380, 643, 892, 131, 252, 771, 764, 259, 508, 515,   1020, 3, 2, 1021, 514, 509, 258, 765, 770, 253, 130, 893, 642, 381, 386,   637, 898, 125, 66, 957, 578, 445, 322, 701, 834, 189, 194, 829, 706, 317,   450, 573, 962, 61, 34, 989, 546, 477, 290, 733, 802, 221, 162, 861, 674,   349, 418, 605, 930, 93, 98, 925, 610, 413, 354, 669, 866, 157, 226, 797,   738, 285, 482, 541, 994, 29, 18, 1005, 530, 493, 274, 749, 786, 237, 146,   877, 658, 365, 402, 621, 914, 109, 82, 941, 594, 429, 338, 685, 850, 173,   210, 813, 722, 301, 466, 557, 978, 45, 50, 973, 562, 461, 306, 717, 818,   205, 178, 845, 690, 333, 434, 589, 946, 77, 114, 909, 626, 397, 370, 653,   882, 141, 242, 781, 754, 269, 498, 525, 1010, 13, 10, 1013, 522, 501, 266,