168 lines
13 KiB
C++
168 lines
13 KiB
C++
// Fill out your copyright notice in the Description page of Project Settings.
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#include "Fixed.h"
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const FFixed FFixed::Unit = FFixed::FromBit(1);
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const FFixed FFixed::Pi = FFixed::FromBit(12868);
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namespace
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{
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constexpr int64 TanTable[] =
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{
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0, 6, 13, 19, 25, 31, 38, 44, 50, 57, 63, 69, 75, 82, 88, 94, 101, 107, 113, 119, 126, 132, 138, 145, 151,
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157, 163, 170, 176, 182, 189, 195, 201, 208, 214, 220, 226, 233, 239, 245, 252, 258, 264, 271, 277, 283, 290,
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296, 302, 308, 315, 321, 327, 334, 340, 346, 353, 359, 365, 372, 378, 384, 391, 397, 403, 410, 416, 422, 429,
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435, 442, 448, 454, 461, 467, 473, 480, 486, 492, 499, 505, 512, 518, 524, 531, 537, 544, 550, 556, 563, 569,
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576, 582, 588, 595, 601, 608, 614, 620, 627, 633, 640, 646, 653, 659, 665, 672, 678, 685, 691, 698, 704, 711,
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717, 724, 730, 737, 743, 750, 756, 763, 769, 776, 782, 789, 795, 802, 808, 815, 821, 828, 834, 841, 847, 854,
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861, 867, 874, 880, 887, 893, 900, 907, 913, 920, 926, 933, 940, 946, 953, 959, 966, 973, 979, 986, 993, 999,
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1006, 1013, 1019, 1026, 1033, 1039, 1046, 1053, 1059, 1066, 1073, 1080, 1086, 1093, 1100, 1107, 1113, 1120, 1127,
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1134, 1140, 1147, 1154, 1161, 1167, 1174, 1181, 1188, 1195, 1201, 1208, 1215, 1222, 1229, 1236, 1243, 1249, 1256,
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1263, 1270, 1277, 1284, 1291, 1298, 1305, 1311, 1318, 1325, 1332, 1339, 1346, 1353, 1360, 1367, 1374, 1381, 1388,
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1395, 1402, 1409, 1416, 1423, 1430, 1437, 1444, 1451, 1458, 1466, 1473, 1480, 1487, 1494, 1501, 1508, 1515, 1523,
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1530, 1537, 1544, 1551, 1558, 1566, 1573, 1580, 1587, 1594, 1602, 1609, 1616, 1623, 1631, 1638, 1645, 1653, 1660,
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1667, 1675, 1682, 1689, 1697, 1704, 1711, 1719, 1726, 1734, 1741, 1748, 1756, 1763, 1771, 1778, 1786, 1793, 1801,
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1808, 1816, 1823, 1831, 1838, 1846, 1853, 1861, 1869, 1876, 1884, 1891, 1899, 1907, 1914, 1922, 1930, 1937, 1945,
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1953, 1960, 1968, 1976, 1984, 1991, 1999, 2007, 2015, 2023, 2030, 2038, 2046, 2054, 2062, 2070, 2078, 2085, 2093,
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2101, 2109, 2117, 2125, 2133, 2141, 2149, 2157, 2165, 2173, 2181, 2189, 2197, 2206, 2214, 2222, 2230, 2238, 2246,
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2254, 2263, 2271, 2279, 2287, 2296, 2304, 2312, 2320, 2329, 2337, 2345, 2354, 2362, 2370, 2379, 2387, 2396, 2404,
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2413, 2421, 2429, 2438, 2447, 2455, 2464, 2472, 2481, 2489, 2498, 2507, 2515, 2524, 2533, 2541, 2550, 2559, 2567,
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2576, 2585, 2594, 2603, 2611, 2620, 2629, 2638, 2647, 2656, 2665, 2674, 2683, 2692, 2701, 2710, 2719, 2728, 2737,
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2746, 2755, 2764, 2773, 2783, 2792, 2801, 2810, 2819, 2829, 2838, 2847, 2857, 2866, 2875, 2885, 2894, 2904, 2913,
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2922, 2932, 2941, 2951, 2961, 2970, 2980, 2989, 2999, 3009, 3018, 3028, 3038, 3048, 3057, 3067, 3077, 3087, 3097,
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3107, 3116, 3126, 3136, 3146, 3156, 3166, 3176, 3186, 3197, 3207, 3217, 3227, 3237, 3247, 3258, 3268, 3278, 3289,
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3299, 3309, 3320, 3330, 3341, 3351, 3362, 3372, 3383, 3393, 3404, 3414, 3425, 3436, 3446, 3457, 3468, 3479, 3490,
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3500, 3511, 3522, 3533, 3544, 3555, 3566, 3577, 3588, 3600, 3611, 3622, 3633, 3644, 3656, 3667, 3678, 3690, 3701,
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3712, 3724, 3735, 3747, 3758, 3770, 3782, 3793, 3805, 3817, 3828, 3840, 3852, 3864, 3876, 3888, 3900, 3912, 3924,
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3936, 3948, 3960, 3972, 3984, 3997, 4009, 4021, 4034, 4046, 4058, 4071, 4083, 4096, 4109, 4121, 4134, 4147, 4159,
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4172, 4185, 4198, 4211, 4224, 4237, 4250, 4263, 4276, 4289, 4302, 4315, 4329, 4342, 4355, 4369, 4382, 4396, 4409,
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4423, 4436, 4450, 4464, 4478, 4491, 4505, 4519, 4533, 4547, 4561, 4575, 4589, 4604, 4618, 4632, 4647, 4661, 4675,
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4690, 4704, 4719, 4734, 4748, 4763, 4778, 4793, 4808, 4823, 4838, 4853, 4868, 4883, 4898, 4914, 4929, 4944, 4960,
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4975, 4991, 5007, 5022, 5038, 5054, 5070, 5086, 5102, 5118, 5134, 5150, 5166, 5183, 5199, 5215, 5232, 5249, 5265,
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5282, 5299, 5315, 5332, 5349, 5366, 5383, 5401, 5418, 5435, 5453, 5470, 5488, 5505, 5523, 5541, 5558, 5576, 5594,
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5612, 5630, 5649, 5667, 5685, 5704, 5722, 5741, 5759, 5778, 5797, 5816, 5835, 5854, 5873, 5892, 5912, 5931, 5951,
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5970, 5990, 6010, 6029, 6049, 6069, 6090, 6110, 6130, 6151, 6171, 6192, 6212, 6233, 6254, 6275, 6296, 6317, 6338,
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6360, 6381, 6403, 6425, 6446, 6468, 6490, 6512, 6535, 6557, 6579, 6602, 6625, 6647, 6670, 6693, 6716, 6740, 6763,
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6786, 6810, 6834, 6858, 6882, 6906, 6930, 6954, 6979, 7003, 7028, 7053, 7078, 7103, 7128, 7153, 7179, 7205, 7230,
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7256, 7282, 7309, 7335, 7362, 7388, 7415, 7442, 7469, 7496, 7524, 7551, 7579, 7607, 7635, 7663, 7691, 7720, 7749,
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7777, 7807, 7836, 7865, 7895, 7924, 7954, 7984, 8015, 8045, 8076, 8106, 8137, 8169, 8200, 8231, 8263, 8295, 8327,
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8360, 8392, 8425, 8458, 8491, 8525, 8558, 8592, 8626, 8660, 8695, 8729, 8764, 8800, 8835, 8871, 8906, 8943, 8979,
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9016, 9052, 9089, 9127, 9164, 9202, 9240, 9279, 9317, 9356, 9396, 9435, 9475, 9515, 9555, 9596, 9637, 9678, 9720,
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9761, 9803, 9846, 9889, 9932, 9975, 10019, 10063, 10107, 10152, 10197, 10242, 10288, 10334, 10381, 10427, 10475,
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10522, 10570, 10618, 10667, 10716, 10766, 10816, 10866, 10917, 10968, 11019, 11071, 11124, 11177, 11230, 11284,
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11338, 11392, 11448, 11503, 11559, 11616, 11673, 11730, 11788, 11847, 11906, 11966, 12026, 12087, 12148, 12210,
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12272, 12335, 12399, 12463, 12528, 12593, 12659, 12726, 12793, 12861, 12929, 12999, 13068, 13139, 13210, 13282,
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13355, 13429, 13503, 13578, 13653, 13730, 13807, 13885, 13964, 14044, 14124, 14206, 14288, 14371, 14455, 14540,
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14626, 14713, 14801, 14890, 14980, 15071, 15162, 15255, 15349, 15444, 15540, 15638, 15736, 15836, 15937, 16039,
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16142, 16246, 16352, 16459, 16568, 16677, 16789, 16901, 17015, 17131, 17247, 17366, 17486, 17607, 17731, 17856,
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17982, 18110, 18240, 18372, 18506, 18641, 18779, 18918, 19059, 19203, 19348, 19496, 19645, 19797, 19951, 20108,
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20267, 20428, 20592, 20758, 20927, 21099, 21273, 21451, 21631, 21814, 22000, 22189, 22381, 22576, 22775, 22978,
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23183, 23393, 23606, 23823, 24044, 24268, 24497, 24730, 24968, 25210, 25457, 25708, 25964, 26226, 26492, 26764,
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27041, 27324, 27613, 27908, 28209, 28517, 28831, 29152, 29480, 29815, 30158, 30509, 30868, 31236, 31612, 31997,
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32391, 32795, 33209, 33634, 34070, 34516, 34975, 35445, 35928, 36425, 36935, 37459, 37999, 38554, 39125, 39713,
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40319, 40943, 41587, 42252, 42937, 43646, 44377, 45134, 45916, 46726, 47564, 48433, 49335, 50270, 51241, 52250,
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53299, 54391, 55528, 56714, 57951, 59243, 60594, 62007, 63488, 65040, 66671, 68384, 70188, 72089, 74096, 76217,
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78463, 80845, 83376, 86070, 88943, 92014, 95305, 98839, 102645, 106755, 111207, 116046, 121326, 127107, 133467,
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140496, 148305, 157034, 166853, 177980, 190698, 205371, 222490, 242720, 266997, 296667, 333755, 381439, 445017,
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534025, 667536, 890053, 1335084, 2670175,
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};
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constexpr int64 CosTable[] =
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{
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4096, 4096, 4096, 4096, 4096, 4096, 4096, 4096, 4096, 4096, 4096, 4095, 4095, 4095, 4095, 4095, 4095, 4095, 4094,
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4094, 4094, 4094, 4094, 4093, 4093, 4093, 4093, 4092, 4092, 4092, 4092, 4091, 4091, 4091, 4090, 4090, 4090, 4089,
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4089, 4089, 4088, 4088, 4088, 4087, 4087, 4086, 4086, 4085, 4085, 4084, 4084, 4083, 4083, 4082, 4082, 4081, 4081,
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4080, 4080, 4079, 4079, 4078, 4077, 4077, 4076, 4076, 4075, 4074, 4074, 4073, 4072, 4072, 4071, 4070, 4070, 4069,
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4068, 4067, 4067, 4066, 4065, 4064, 4064, 4063, 4062, 4061, 4060, 4060, 4059, 4058, 4057, 4056, 4055, 4054, 4053,
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4053, 4052, 4051, 4050, 4049, 4048, 4047, 4046, 4045, 4044, 4043, 4042, 4041, 4040, 4039, 4038, 4037, 4036, 4035,
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4034, 4032, 4031, 4030, 4029, 4028, 4027, 4026, 4024, 4023, 4022, 4021, 4020, 4019, 4017, 4016, 4015, 4014, 4012,
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4011, 4010, 4008, 4007, 4006, 4005, 4003, 4002, 4001, 3999, 3998, 3996, 3995, 3994, 3992, 3991, 3989, 3988, 3987,
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3985, 3984, 3982, 3981, 3979, 3978, 3976, 3975, 3973, 3972, 3970, 3969, 3967, 3965, 3964, 3962, 3961, 3959, 3958,
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3956, 3954, 3953, 3951, 3949, 3948, 3946, 3944, 3943, 3941, 3939, 3937, 3936, 3934, 3932, 3930, 3929, 3927, 3925,
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3923, 3921, 3920, 3918, 3916, 3914, 3912, 3910, 3909, 3907, 3905, 3903, 3901, 3899, 3897, 3895, 3893, 3891, 3889,
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3887, 3885, 3883, 3881, 3879, 3877, 3875, 3873, 3871, 3869, 3867, 3865, 3863, 3861, 3859, 3857, 3854, 3852, 3850,
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3848, 3846, 3844, 3842, 3839, 3837, 3835, 3833, 3831, 3828, 3826, 3824, 3822, 3819, 3817, 3815, 3812, 3810, 3808,
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3805, 3803, 3801, 3798, 3796, 3794, 3791, 3789, 3787, 3784, 3782, 3779, 3777, 3775, 3772, 3770, 3767, 3765, 3762,
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3760, 3757, 3755, 3752, 3750, 3747, 3745, 3742, 3739, 3737, 3734, 3732, 3729, 3727, 3724, 3721, 3719, 3716, 3713,
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3711, 3708, 3705, 3703, 3700, 3697, 3695, 3692, 3689, 3686, 3684, 3681, 3678, 3675, 3673, 3670, 3667, 3664, 3661,
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3659, 3656, 3653, 3650, 3647, 3644, 3642, 3639, 3636, 3633, 3630, 3627, 3624, 3621, 3618, 3615, 3612, 3609, 3606,
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3603, 3600, 3597, 3594, 3591, 3588, 3585, 3582, 3579, 3576, 3573, 3570, 3567, 3564, 3561, 3558, 3555, 3551, 3548,
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3545, 3542, 3539, 3536, 3532, 3529, 3526, 3523, 3520, 3516, 3513, 3510, 3507, 3504, 3500, 3497, 3494, 3490, 3487,
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3484, 3481, 3477, 3474, 3471, 3467, 3464, 3461, 3457, 3454, 3450, 3447, 3444, 3440, 3437, 3433, 3430, 3426, 3423,
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3420, 3416, 3413, 3409, 3406, 3402, 3399, 3395, 3392, 3388, 3385, 3381, 3378, 3374, 3370, 3367, 3363, 3360, 3356,
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3352, 3349, 3345, 3342, 3338, 3334, 3331, 3327, 3323, 3320, 3316, 3312, 3309, 3305, 3301, 3297, 3294, 3290, 3286,
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3282, 3279, 3275, 3271, 3267, 3264, 3260, 3256, 3252, 3248, 3244, 3241, 3237, 3233, 3229, 3225, 3221, 3217, 3214,
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3210, 3206, 3202, 3198, 3194, 3190, 3186, 3182, 3178, 3174, 3170, 3166, 3162, 3158, 3154, 3150, 3146, 3142, 3138,
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3134, 3130, 3126, 3122, 3118, 3114, 3110, 3106, 3102, 3097, 3093, 3089, 3085, 3081, 3077, 3073, 3068, 3064, 3060,
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3056, 3052, 3048, 3043, 3039, 3035, 3031, 3026, 3022, 3018, 3014, 3009, 3005, 3001, 2997, 2992, 2988, 2984, 2979,
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2975, 2971, 2967, 2962, 2958, 2953, 2949, 2945, 2940, 2936, 2932, 2927, 2923, 2918, 2914, 2910, 2905, 2901, 2896,
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2892, 2887, 2883, 2878, 2874, 2870, 2865, 2861, 2856, 2852, 2847, 2843, 2838, 2833, 2829, 2824, 2820, 2815, 2811,
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2806, 2802, 2797, 2792, 2788, 2783, 2779, 2774, 2769, 2765, 2760, 2755, 2751, 2746, 2741, 2737, 2732, 2727, 2723,
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2718, 2713, 2709, 2704, 2699, 2694, 2690, 2685, 2680, 2675, 2671, 2666, 2661, 2656, 2652, 2647, 2642, 2637, 2632,
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2628, 2623, 2618, 2613, 2608, 2603, 2598, 2594, 2589, 2584, 2579, 2574, 2569, 2564, 2559, 2555, 2550, 2545, 2540,
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2535, 2530, 2525, 2520, 2515, 2510, 2505, 2500, 2495, 2490, 2485, 2480, 2475, 2470, 2465, 2460, 2455, 2450, 2445,
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2440, 2435, 2430, 2425, 2420, 2415, 2410, 2405, 2399, 2394, 2389, 2384, 2379, 2374, 2369, 2364, 2359, 2353, 2348,
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2343, 2338, 2333, 2328, 2322, 2317, 2312, 2307, 2302, 2296, 2291, 2286, 2281, 2276, 2270, 2265, 2260, 2255, 2249,
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2244, 2239, 2234, 2228, 2223, 2218, 2213, 2207, 2202, 2197, 2191, 2186, 2181, 2175, 2170, 2165, 2159, 2154, 2149,
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2143, 2138, 2133, 2127, 2122, 2117, 2111, 2106, 2100, 2095, 2090, 2084, 2079, 2073, 2068, 2062, 2057, 2052, 2046,
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2041, 2035, 2030, 2024, 2019, 2013, 2008, 2002, 1997, 1992, 1986, 1981, 1975, 1970, 1964, 1958, 1953, 1947, 1942,
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1936, 1931, 1925, 1920, 1914, 1909, 1903, 1898, 1892, 1886, 1881, 1875, 1870, 1864, 1858, 1853, 1847, 1842, 1836,
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1830, 1825, 1819, 1813, 1808, 1802, 1797, 1791, 1785, 1780, 1774, 1768, 1763, 1757, 1751, 1746, 1740, 1734, 1729,
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1723, 1717, 1711, 1706, 1700, 1694, 1689, 1683, 1677, 1671, 1666, 1660, 1654, 1648, 1643, 1637, 1631, 1625, 1620,
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1614, 1608, 1602, 1596, 1591, 1585, 1579, 1573, 1567, 1562, 1556, 1550, 1544, 1538, 1533, 1527, 1521, 1515, 1509,
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1503, 1498, 1492, 1486, 1480, 1474, 1468, 1462, 1457, 1451, 1445, 1439, 1433, 1427, 1421, 1415, 1409, 1404, 1398,
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1392, 1386, 1380, 1374, 1368, 1362, 1356, 1350, 1344, 1338, 1332, 1327, 1321, 1315, 1309, 1303, 1297, 1291, 1285,
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1279, 1273, 1267, 1261, 1255, 1249, 1243, 1237, 1231, 1225, 1219, 1213, 1207, 1201, 1195, 1189, 1183, 1177, 1171,
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1165, 1159, 1153, 1147, 1141, 1135, 1129, 1123, 1117, 1111, 1105, 1099, 1092, 1086, 1080, 1074, 1068, 1062, 1056,
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1050, 1044, 1038, 1032, 1026, 1020, 1014, 1007, 1001, 995, 989, 983, 977, 971, 965, 959, 953, 946, 940, 934, 928,
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922, 916, 910, 904, 897, 891, 885, 879, 873, 867, 861, 854, 848, 842, 836, 830, 824, 818, 811, 805, 799, 793, 787,
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781, 774, 768, 762, 756, 750, 744, 737, 731, 725, 719, 713, 706, 700, 694, 688, 682, 675, 669, 663, 657, 651, 644,
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638, 632, 626, 620, 613, 607, 601, 595, 589, 582, 576, 570, 564, 557, 551, 545, 539, 533, 526, 520, 514, 508, 501,
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495, 489, 483, 476, 470, 464, 458, 451, 445, 439, 433, 426, 420, 414, 408, 401, 395, 389, 383, 376, 370, 364, 358,
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351, 345, 339, 333, 326, 320, 314, 308, 301, 295, 289, 283, 276, 270, 264, 257, 251, 245, 239, 232, 226, 220, 214,
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207, 201, 195, 188, 182, 176, 170, 163, 157, 151, 144, 138, 132, 126, 119, 113, 107, 101, 94, 88, 82, 75, 69, 63,
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57, 50, 44, 38, 31, 25, 19, 13, 6,
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};
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}
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FFixed FFixedMath::TanUnit(FFixed A)
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{
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FFixed Result;
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bool Signed = A.Data < 0;
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A.Data = FMath::Abs(A.Data);
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int64 Temp = A.Data % 2048;
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if (Temp == 1024) Result.Data = INT64_MAX;
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else if (Temp < 1024)
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Result.Data = TanTable[Temp];
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else
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Result.Data = -TanTable[2048 - Temp];
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Result.Data *= Signed ? -1 : 1;
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return Result;
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}
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FFixed FFixedMath::SinUnit(FFixed A)
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{
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FFixed Quarter;
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Quarter.Data = 1024;
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return CosUnit(A - Quarter);
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}
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FFixed FFixedMath::CosUnit(FFixed A)
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{
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FFixed Result;
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A.Data = FMath::Abs(A.Data);
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int64 Temp = A.Data % 2048;
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bool Signed = A.Data % 4096 < 2048;
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if (Temp == 1024) Result.Data = 0;
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else if (Signed && Temp < 1024)
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Result.Data = CosTable[Temp];
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else if (Signed && Temp >= 1024)
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Result.Data = -CosTable[2048 - Temp];
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else if (Temp < 1024)
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Result.Data = -CosTable[Temp];
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else
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Result.Data = CosTable[2048 - Temp];
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return Result;
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}
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