newfct.cpp

普林斯顿开发的快速球面调和变换算法

  3077, 3066, 1029, 2042, 2053, 4090, 5, 6, 4089, 2054, 2041, 1030, 3065, 
  3078, 1017, 518, 3577, 2566, 1529, 1542, 2553, 3590, 505, 262, 3833, 2310, 
  1785, 1286, 2809, 3334, 761, 774, 3321, 2822, 1273, 1798, 2297, 3846, 249, 
  134, 3961, 2182, 1913, 1158, 2937, 3206, 889, 646, 3449, 2694, 1401, 1670, 
  2425, 3718, 377, 390, 3705, 2438, 1657, 1414, 2681, 3462, 633, 902, 3193, 
  2950, 1145, 1926, 2169, 3974, 121, 70, 4025, 2118, 1977, 1094, 3001, 3142, 
  953, 582, 3513, 2630, 1465, 1606, 2489, 3654, 441, 326, 3769, 2374, 1721, 
  1350, 2745, 3398, 697, 838, 3257, 2886, 1209, 1862, 2233, 3910, 185, 198, 
  3897, 2246, 1849, 1222, 2873, 3270, 825, 710, 3385, 2758, 1337, 1734, 2361, 
  3782, 313, 454, 3641, 2502, 1593, 1478, 2617, 3526, 569, 966, 3129, 3014, 
  1081, 1990, 2105, 4038, 57, 38, 4057, 2086, 2009, 1062, 3033, 3110, 985, 
  550, 3545, 2598, 1497, 1574, 2521, 3622, 473, 294, 3801, 2342, 1753, 1318, 
  2777, 3366, 729, 806, 3289, 2854, 1241, 1830, 2265, 3878, 217, 166, 3929, 
  2214, 1881, 1190, 2905, 3238, 857, 678, 3417, 2726, 1369, 1702, 2393, 3750, 
  345, 422, 3673, 2470, 1625, 1446, 2649, 3494, 601, 934, 3161, 2982, 1113, 
  1958, 2137, 4006, 89, 102, 3993, 2150, 1945, 1126, 2969, 3174, 921, 614, 
  3481, 2662, 1433, 1638, 2457, 3686, 409, 358, 3737, 2406, 1689, 1382, 2713, 
  3430, 665, 870, 3225, 2918, 1177, 1894, 2201, 3942, 153, 230, 3865, 2278, 
  1817, 1254, 2841, 3302, 793, 742, 3353, 2790, 1305, 1766, 2329, 3814, 281, 
  486, 3609, 2534, 1561, 1510, 2585, 3558, 537, 998, 3097, 3046, 1049, 2022, 
  2073, 4070, 25, 22, 4073, 2070, 2025, 1046, 3049, 3094, 1001, 534, 3561, 
  2582, 1513, 1558, 2537, 3606, 489, 278, 3817, 2326, 1769, 1302, 2793, 3350, 
  745, 790, 3305, 2838, 1257, 1814, 2281, 3862, 233, 150, 3945, 2198, 1897, 
  1174, 2921, 3222, 873, 662, 3433, 2710, 1385, 1686, 2409, 3734, 361, 406, 
  3689, 2454, 1641, 1430, 2665, 3478, 617, 918, 3177, 2966, 1129, 1942, 2153, 
  3990, 105, 86, 4009, 2134, 1961, 1110, 2985, 3158, 937, 598, 3497, 2646, 
  1449, 1622, 2473, 3670, 425, 342, 3753, 2390, 1705, 1366, 2729, 3414, 681, 
  854, 3241, 2902, 1193, 1878, 2217, 3926, 169, 214, 3881, 2262, 1833, 1238, 
  2857, 3286, 809, 726, 3369, 2774, 1321, 1750, 2345, 3798, 297, 470, 3625, 
  2518, 1577, 1494, 2601, 3542, 553, 982, 3113, 3030, 1065, 2006, 2089, 4054, 
  41, 54, 4041, 2102, 1993, 1078, 3017, 3126, 969, 566, 3529, 2614, 1481, 
  1590, 2505, 3638, 457, 310, 3785, 2358, 1737, 1334, 2761, 3382, 713, 822, 
  3273, 2870, 1225, 1846, 2249, 3894, 201, 182, 3913, 2230, 1865, 1206, 2889, 
  3254, 841, 694, 3401, 2742, 1353, 1718, 2377, 3766, 329, 438, 3657, 2486, 
  1609, 1462, 2633, 3510, 585, 950, 3145, 2998, 1097, 1974, 2121, 4022, 73, 
  118, 3977, 2166, 1929, 1142, 2953, 3190, 905, 630, 3465, 2678, 1417, 1654, 
  2441, 3702, 393, 374, 3721, 2422, 1673, 1398, 2697, 3446, 649, 886, 3209, 
  2934, 1161, 1910, 2185, 3958, 137, 246, 3849, 2294, 1801, 1270, 2825, 3318, 
  777, 758, 3337, 2806, 1289, 1782, 2313, 3830, 265, 502, 3593, 2550, 1545, 
  1526, 2569, 3574, 521, 1014, 3081, 3062, 1033, 2038, 2057, 4086, 9, 14, 
  4081, 2062, 2033, 1038, 3057, 3086, 1009, 526, 3569, 2574, 1521, 1550, 
  2545, 3598, 497, 270, 3825, 2318, 1777, 1294, 2801, 3342, 753, 782, 3313, 
  2830, 1265, 1806, 2289, 3854, 241, 142, 3953, 2190, 1905, 1166, 2929, 3214, 
  881, 654, 3441, 2702, 1393, 1678, 2417, 3726, 369, 398, 3697, 2446, 1649, 
  1422, 2673, 3470, 625, 910, 3185, 2958, 1137, 1934, 2161, 3982, 113, 78, 
  4017, 2126, 1969, 1102, 2993, 3150, 945, 590, 3505, 2638, 1457, 1614, 2481, 
  3662, 433, 334, 3761, 2382, 1713, 1358, 2737, 3406, 689, 846, 3249, 2894, 
  1201, 1870, 2225, 3918, 177, 206, 3889, 2254, 1841, 1230, 2865, 3278, 817, 
  718, 3377, 2766, 1329, 1742, 2353, 3790, 305, 462, 3633, 2510, 1585, 1486, 
  2609, 3534, 561, 974, 3121, 3022, 1073, 1998, 2097, 4046, 49, 46, 4049, 
  2094, 2001, 1070, 3025, 3118, 977, 558, 3537, 2606, 1489, 1582, 2513, 3630, 
  465, 302, 3793, 2350, 1745, 1326, 2769, 3374, 721, 814, 3281, 2862, 1233, 
  1838, 2257, 3886, 209, 174, 3921, 2222, 1873, 1198, 2897, 3246, 849, 686, 
  3409, 2734, 1361, 1710, 2385, 3758, 337, 430, 3665, 2478, 1617, 1454, 2641, 
  3502, 593, 942, 3153, 2990, 1105, 1966, 2129, 4014, 81, 110, 3985, 2158, 
  1937, 1134, 2961, 3182, 913, 622, 3473, 2670, 1425, 1646, 2449, 3694, 401, 
  366, 3729, 2414, 1681, 1390, 2705, 3438, 657, 878, 3217, 2926, 1169, 1902, 
  2193, 3950, 145, 238, 3857, 2286, 1809, 1262, 2833, 3310, 785, 750, 3345, 
  2798, 1297, 1774, 2321, 3822, 273, 494, 3601, 2542, 1553, 1518, 2577, 3566, 
  529, 1006, 3089, 3054, 1041, 2030, 2065, 4078, 17, 30, 4065, 2078, 2017, 
  1054, 3041, 3102, 993, 542, 3553, 2590, 1505, 1566, 2529, 3614, 481, 286, 
  3809, 2334, 1761, 1310, 2785, 3358, 737, 798, 3297, 2846, 1249, 1822, 2273, 
  3870, 225, 158, 3937, 2206, 1889, 1182, 2913, 3230, 865, 670, 3425, 2718, 
  1377, 1694, 2401, 3742, 353, 414, 3681, 2462, 1633, 1438, 2657, 3486, 609, 
  926, 3169, 2974, 1121, 1950, 2145, 3998, 97, 94, 4001, 2142, 1953, 1118, 
  2977, 3166, 929, 606, 3489, 2654, 1441, 1630, 2465, 3678, 417, 350, 3745, 
  2398, 1697, 1374, 2721, 3422, 673, 862, 3233, 2910, 1185, 1886, 2209, 3934, 
  161, 222, 3873, 2270, 1825, 1246, 2849, 3294, 801, 734, 3361, 2782, 1313, 
  1758, 2337, 3806, 289, 478, 3617, 2526, 1569, 1502, 2593, 3550, 545, 990, 
  3105, 3038, 1057, 2014, 2081, 4062, 33, 62, 4033, 2110, 1985, 1086, 3009, 
  3134, 961, 574, 3521, 2622, 1473, 1598, 2497, 3646, 449, 318, 3777, 2366, 
  1729, 1342, 2753, 3390, 705, 830, 3265, 2878, 1217, 1854, 2241, 3902, 193, 
  190, 3905, 2238, 1857, 1214, 2881, 3262, 833, 702, 3393, 2750, 1345, 1726, 
  2369, 3774, 321, 446, 3649, 2494, 1601, 1470, 2625, 3518, 577, 958, 3137, 
  3006, 1089, 1982, 2113, 4030, 65, 126, 3969, 2174, 1921, 1150, 2945, 3198, 
  897, 638, 3457, 2686, 1409, 1662, 2433, 3710, 385, 382, 3713, 2430, 1665, 
  1406, 2689, 3454, 641, 894, 3201, 2942, 1153, 1918, 2177, 3966, 129, 254, 
  3841, 2302, 1793, 1278, 2817, 3326, 769, 766, 3329, 2814, 1281, 1790, 2305, 
  3838, 257, 510, 3585, 2558, 1537, 1534, 2561, 3582, 513, 1022, 3073, 3070, 
  1025, 2046, 2049, 4094, 1};

  static const double mod2[2] = {-0.7071067811865475, 0.7071067811865475};

static const double mod4[4] = 
{-0.923879532511287, 0.923879532511287, 0.3826834323650897, 
  -0.3826834323650898};

static const double mod8[8] = 
{-0.98078528040323, 0.98078528040323, 0.1950903220161282, 
  -0.1950903220161283, -0.5555702330196023, 0.555570233019602, 
  0.831469612302545, -0.831469612302545};

static const double mod16[16] = 
{-0.995184726672197, 0.995184726672197, 0.0980171403295607, 
  -0.0980171403295608, -0.6343932841636457, 0.6343932841636453, 
  0.7730104533627369, -0.773010453362737, -0.881921264348355, 
  0.881921264348355, 0.4713967368259978, -0.4713967368259978, 
  -0.2902846772544623, 0.2902846772544622, 0.956940335732209, 
  -0.956940335732209};

static const double mod32[32] =
{-0.998795456205172, 0.998795456205172, 0.04906767432741801, 
  -0.04906767432741814, -0.6715589548470185, 0.6715589548470185, 
  0.7409511253549589, -0.7409511253549593, -0.903989293123443, 
  0.903989293123443, 0.4275550934302819, -0.4275550934302822, 
  -0.33688985339222, 0.3368898533922199, 0.941544065183021, 
  -0.941544065183021, -0.970031253194544, 0.970031253194544, 
  0.2429801799032639, -0.242980179903264, -0.5141027441932219, 
  0.5141027441932216, 0.857728610000272, -0.857728610000272, 
  -0.803207531480645, 0.803207531480645, 0.5956993044924333, 
  -0.5956993044924336, -0.1467304744553617, 0.1467304744553616, 
  0.989176509964781, -0.989176509964781};

static const double mod64[64] =
{-0.999698818696204, 0.999698818696204, 0.02454122852291214, 
  -0.02454122852291227, -0.689540544737067, 0.6895405447370669, 
  0.7242470829514668, -0.7242470829514671, -0.914209755703531, 
  0.914209755703531, 0.4052413140049898, -0.4052413140049899, 
  -0.3598950365349883, 0.3598950365349882, 0.932992798834739, 
  -0.932992798834739, -0.975702130038529, 0.975702130038528, 
  0.2191012401568697, -0.2191012401568698, -0.5349976198870974, 
  0.534997619887097, 0.844853565249707, -0.844853565249707, 
  -0.817584813151584, 0.817584813151584, 0.5758081914178454, 
  -0.5758081914178455, -0.1709618887603014, 0.1709618887603012, 
  0.985277642388941, -0.985277642388941, -0.99247953459871, 0.99247953459871, 
  0.1224106751992162, -0.1224106751992163, -0.6152315905806269, 
  0.6152315905806267, 0.7883464276266061, -0.7883464276266064, 
  -0.870086991108711, 0.870086991108711, 0.492898192229784, 
  -0.4928981922297842, -0.2667127574748984, 0.2667127574748983, 
  0.96377606579544, -0.96377606579544, -0.949528180593037, 0.949528180593037, 
  0.3136817403988914, -0.3136817403988915, -0.4496113296546067, 
  0.4496113296546067, 0.893224301195515, -0.893224301195515, 
  -0.7572088465064847, 0.7572088465064847, 0.6531728429537766, 
  -0.6531728429537769, -0.07356456359966746, 0.07356456359966735, 
  0.99729045667869, -0.99729045667869};

static const double mod128[128] =
{-0.999924701839145, 0.999924701839145, 0.01227153828571982, 
  -0.01227153828571994, -0.698376249408973, 0.6983762494089728, 
  0.7157308252838185, -0.7157308252838188, -0.919113851690058, 
  0.919113851690058, 0.393992040061048, -0.3939920400610481, 
  -0.3713171939518376, 0.3713171939518375, 0.928506080473215, 
  -0.928506080473215, -0.978317370719628, 0.978317370719628, 
  0.2071113761922184, -0.2071113761922186, -0.5453249884220466, 
  0.5453249884220462, 0.838224705554838, -0.838224705554838, 
  -0.824589302785025, 0.824589302785025, 0.5657318107836132, 
  -0.5657318107836132, -0.183039887955141, 0.1830398879551409, 
  0.983105487431216, -0.983105487431216, -0.993906970002356, 
  0.993906970002356, 0.1102222072938831, -0.1102222072938832, 
  -0.6248594881423865, 0.6248594881423863, 0.7807372285720944, 
  -0.7807372285720945, -0.876070094195407, 0.876070094195407, 
  0.4821837720791227, -0.4821837720791229, -0.278519689385053, 
  0.278519689385053, 0.960430519415566, -0.960430519415566, 
  -0.953306040354194, 0.953306040354194, 0.3020059493192281, 
  -0.3020059493192282, -0.4605387109582401, 0.4605387109582402, 
  0.887639620402854, -0.887639620402854, -0.765167265622459, 
  0.765167265622459, 0.6438315428897913, -0.6438315428897915, 
  -0.0857973123444399, 0.0857973123444398, 0.996312612182778, 
  -0.996312612182778, -0.998118112900149, 0.998118112900149, 
  0.06132073630220854, -0.06132073630220866, -0.6624157775901719, 
  0.6624157775901719, 0.7491363945234591, -0.7491363945234594, 
  -0.898674465693954, 0.898674465693954, 0.4386162385385274, 
  -0.4386162385385277, -0.325310292162263, 0.3253102921622629, 
  0.945607325380521, -0.945607325380521, -0.966976471044852, 
  0.966976471044852, 0.2548656596045145, -0.2548656596045146, 
  -0.5035383837257176, 0.5035383837257175, 0.863972856121587, 
  -0.863972856121587, -0.7958369046088836, 0.7958369046088835, 
  0.6055110414043254, -0.6055110414043256, -0.1345807085071262, 
  0.1345807085071261, 0.99090263542778, -0.99090263542778, 
  -0.987301418157858, 0.987301418157858, 0.1588581433338613, 
  -0.1588581433338614, -0.5857978574564389, 0.5857978574564389, 
  0.810457198252595, -0.810457198252595, -0.851355193105265, 
  0.851355193105265, 0.5245896826784687, -0.524589682678469, 
  -0.2310581082806713, 0.2310581082806711, 0.97293995220556, 
  -0.97293995220556, -0.937339011912575, 0.937339011912575, 
  0.3484186802494344, -0.3484186802494345, -0.4164295600976374, 
  0.416429560097637, 0.909167983090523, -0.909167983090523, 
  -0.7326542716724129, 0.7326542716724127, 0.6806009977954531, 
  -0.6806009977954531, -0.03680722294135899, 0.03680722294135887, 
  0.99932238458835, -0.99932238458835};

static const double mod256[256] =
{-0.999981175282601, 0.999981175282601, 0.006135884649154394, 
  -0.006135884649154516, -0.7027547444572254, 0.7027547444572252, 
  0.7114321957452165, -0.7114321957452165, -0.921514039342042, 
  0.921514039342042, 0.3883450466988262, -0.3883450466988263, 
  -0.3770074102164183, 0.3770074102164182, 0.926210242138311, 
  -0.926210242138311, -0.97956976568544, 0.97956976568544,