You.i Engine
YiMathTables.h
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1 // © You i Labs Inc. 2000-2017. All rights reserved.
7 #ifndef _YI_MATH_TABLES_H_
8 #define _YI_MATH_TABLES_H_
9 
10 /*****************************************************************************
11  Square root, Sine, Cosine and Arc Tangent tables
12 *****************************************************************************/
13 
14 const int32_t YI_ANGLESHIFT = 11; // YI_ANGLE2PI = 1 << YI_ANGLESHIFT
15 const int32_t YI_ANGLE2PI = 2048; // equivalent to 2*PI
16 const int32_t YI_ANGLEPI = YI_ANGLE2PI / 2; // equivalent to PI
17 const int32_t YI_ANGLEMASK = YI_ANGLE2PI - 1; // angle mask use to acces trigonometric tables
18 const float YI_PI = 3.1415926535897932384626433832795f; // cherry pie!
19 const int32_t YI_TRIG_SHIFT = 14; // shifted 2^n value for sinus/cosinus result
20 const int32_t YI_TRIG_MUL = 16384; // sinus/cosinus YI_MAX value (==1)
21 const int32_t YI_ATAN_SIZE = (YI_ANGLE2PI / 4);
22 
23 const int16_t g_sYISine[YI_ANGLE2PI] = { 0, 50, 100, 150, 201, 251, 301, 351, 402, 452, 502, 552, 603, 653, 703, 753, 803, 854, 904, 954, 1004, 1054,
24  1105, 1155, 1205, 1255, 1305, 1355, 1405, 1455, 1505, 1555, 1605, 1655, 1705, 1755, 1805, 1855, 1905, 1955, 2005, 2055, 2105, 2155,
25  2204, 2254, 2304, 2354, 2404, 2453, 2503, 2553, 2602, 2652, 2701, 2751, 2801, 2850, 2900, 2949, 2998, 3048, 3097, 3147, 3196, 3245,
26  3294, 3344, 3393, 3442, 3491, 3540, 3589, 3638, 3687, 3736, 3785, 3834, 3883, 3932, 3980, 4029, 4078, 4127, 4175, 4224, 4272, 4321,
27  4369, 4418, 4466, 4514, 4563, 4611, 4659, 4707, 4756, 4804, 4852, 4900, 4948, 4995, 5043, 5091, 5139, 5187, 5234, 5282, 5329, 5377,
28  5424, 5472, 5519, 5566, 5614, 5661, 5708, 5755, 5802, 5849, 5896, 5943, 5990, 6036, 6083, 6130, 6176, 6223, 6269, 6316, 6362, 6408,
29  6455, 6501, 6547, 6593, 6639, 6685, 6731, 6777, 6822, 6868, 6914, 6959, 7005, 7050, 7095, 7141, 7186, 7231, 7276, 7321, 7366, 7411,
30  7456, 7500, 7545, 7590, 7634, 7678, 7723, 7767, 7811, 7856, 7900, 7944, 7988, 8031, 8075, 8119, 8162, 8206, 8249, 8293, 8336, 8379,
31  8423, 8466, 8509, 8552, 8594, 8637, 8680, 8722, 8765, 8807, 8850, 8892, 8934, 8976, 9018, 9060, 9102, 9144, 9185, 9227, 9268, 9310,
32  9351, 9392, 9434, 9475, 9516, 9556, 9597, 9638, 9679, 9719, 9759, 9800, 9840, 9880, 9920, 9960, 10000, 10040, 10079, 10119, 10159, 10198,
33  10237, 10276, 10315, 10354, 10393, 10432, 10471, 10510, 10548, 10586, 10625, 10663, 10701, 10739, 10777, 10815, 10853, 10890, 10928, 10965, 11002, 11040,
34  11077, 11114, 11150, 11187, 11224, 11260, 11297, 11333, 11370, 11406, 11442, 11478, 11513, 11549, 11585, 11620, 11656, 11691, 11726, 11761, 11796, 11831,
35  11866, 11900, 11935, 11969, 12003, 12037, 12072, 12105, 12139, 12173, 12207, 12240, 12273, 12307, 12340, 12373, 12406, 12438, 12471, 12504, 12536, 12568,
36  12600, 12633, 12665, 12696, 12728, 12760, 12791, 12822, 12854, 12885, 12916, 12947, 12977, 13008, 13038, 13069, 13099, 13129, 13159, 13189, 13219, 13249,
37  13278, 13307, 13337, 13366, 13395, 13424, 13452, 13481, 13510, 13538, 13566, 13594, 13622, 13650, 13678, 13705, 13733, 13760, 13788, 13815, 13842, 13868,
38  13895, 13922, 13948, 13974, 14001, 14027, 14053, 14078, 14104, 14129, 14155, 14180, 14205, 14230, 14255, 14280, 14304, 14329, 14353, 14377, 14401, 14425,
39  14449, 14473, 14496, 14519, 14543, 14566, 14589, 14611, 14634, 14657, 14679, 14701, 14723, 14745, 14767, 14789, 14810, 14832, 14853, 14874, 14895, 14916,
40  14937, 14957, 14978, 14998, 15018, 15038, 15058, 15078, 15098, 15117, 15136, 15156, 15175, 15193, 15212, 15231, 15249, 15267, 15286, 15304, 15322, 15339,
41  15357, 15374, 15392, 15409, 15426, 15443, 15459, 15476, 15492, 15509, 15525, 15541, 15557, 15572, 15588, 15603, 15618, 15634, 15649, 15663, 15678, 15693,
42  15707, 15721, 15735, 15749, 15763, 15777, 15790, 15803, 15817, 15830, 15842, 15855, 15868, 15880, 15892, 15905, 15917, 15928, 15940, 15952, 15963, 15974,
43  15985, 15996, 16007, 16018, 16028, 16039, 16049, 16059, 16069, 16078, 16088, 16097, 16107, 16116, 16125, 16134, 16142, 16151, 16159, 16167, 16175, 16183,
44  16191, 16199, 16206, 16213, 16221, 16228, 16234, 16241, 16248, 16254, 16260, 16266, 16272, 16278, 16284, 16289, 16294, 16300, 16305, 16309, 16314, 16319,
45  16323, 16327, 16331, 16335, 16339, 16343, 16346, 16350, 16353, 16356, 16359, 16361, 16364, 16366, 16368, 16370, 16372, 16374, 16376, 16377, 16379, 16380,
46  16381, 16382, 16382, 16383, 16383, 16383, 16383, 16383, 16383, 16383, 16382, 16382, 16381, 16380, 16379, 16377, 16376, 16374, 16372, 16370, 16368, 16366,
47  16364, 16361, 16359, 16356, 16353, 16350, 16346, 16343, 16339, 16335, 16331, 16327, 16323, 16319, 16314, 16309, 16305, 16300, 16294, 16289, 16284, 16278,
48  16272, 16266, 16260, 16254, 16248, 16241, 16234, 16228, 16221, 16213, 16206, 16199, 16191, 16183, 16175, 16167, 16159, 16151, 16142, 16134, 16125, 16116,
49  16107, 16097, 16088, 16078, 16069, 16059, 16049, 16039, 16028, 16018, 16007, 15996, 15985, 15974, 15963, 15952, 15940, 15928, 15917, 15905, 15892, 15880,
50  15868, 15855, 15842, 15830, 15817, 15803, 15790, 15777, 15763, 15749, 15735, 15721, 15707, 15693, 15678, 15663, 15649, 15634, 15618, 15603, 15588, 15572,
51  15557, 15541, 15525, 15509, 15492, 15476, 15459, 15443, 15426, 15409, 15392, 15374, 15357, 15339, 15322, 15304, 15286, 15267, 15249, 15231, 15212, 15193,
52  15175, 15156, 15136, 15117, 15098, 15078, 15058, 15038, 15018, 14998, 14978, 14957, 14937, 14916, 14895, 14874, 14853, 14832, 14810, 14789, 14767, 14745,
53  14723, 14701, 14679, 14657, 14634, 14611, 14589, 14566, 14543, 14519, 14496, 14473, 14449, 14425, 14401, 14377, 14353, 14329, 14304, 14280, 14255, 14230,
54  14205, 14180, 14155, 14129, 14104, 14078, 14053, 14027, 14001, 13974, 13948, 13922, 13895, 13868, 13842, 13815, 13788, 13760, 13733, 13705, 13678, 13650,
55  13622, 13594, 13566, 13538, 13510, 13481, 13452, 13424, 13395, 13366, 13337, 13307, 13278, 13249, 13219, 13189, 13159, 13129, 13099, 13069, 13038, 13008,
56  12977, 12947, 12916, 12885, 12854, 12822, 12791, 12760, 12728, 12696, 12665, 12633, 12600, 12568, 12536, 12504, 12471, 12438, 12406, 12373, 12340, 12307,
57  12273, 12240, 12207, 12173, 12139, 12105, 12072, 12037, 12003, 11969, 11935, 11900, 11866, 11831, 11796, 11761, 11726, 11691, 11656, 11620, 11585, 11549,
58  11513, 11478, 11442, 11406, 11370, 11333, 11297, 11260, 11224, 11187, 11150, 11114, 11077, 11040, 11002, 10965, 10928, 10890, 10853, 10815, 10777, 10739,
59  10701, 10663, 10625, 10586, 10548, 10510, 10471, 10432, 10393, 10354, 10315, 10276, 10237, 10198, 10159, 10119, 10079, 10040, 10000, 9960, 9920, 9880,
60  9840, 9800, 9759, 9719, 9679, 9638, 9597, 9556, 9516, 9475, 9434, 9392, 9351, 9310, 9268, 9227, 9185, 9144, 9102, 9060, 9018, 8976,
61  8934, 8892, 8850, 8807, 8765, 8722, 8680, 8637, 8594, 8552, 8509, 8466, 8423, 8379, 8336, 8293, 8249, 8206, 8162, 8119, 8075, 8031,
62  7988, 7944, 7900, 7856, 7811, 7767, 7723, 7678, 7634, 7590, 7545, 7500, 7456, 7411, 7366, 7321, 7276, 7231, 7186, 7141, 7095, 7050,
63  7005, 6959, 6914, 6868, 6822, 6777, 6731, 6685, 6639, 6593, 6547, 6501, 6455, 6408, 6362, 6316, 6269, 6223, 6176, 6130, 6083, 6036,
64  5990, 5943, 5896, 5849, 5802, 5755, 5708, 5661, 5614, 5566, 5519, 5472, 5424, 5377, 5329, 5282, 5234, 5187, 5139, 5091, 5043, 4995,
65  4948, 4900, 4852, 4804, 4756, 4707, 4659, 4611, 4563, 4514, 4466, 4418, 4369, 4321, 4272, 4224, 4175, 4127, 4078, 4029, 3980, 3932,
66  3883, 3834, 3785, 3736, 3687, 3638, 3589, 3540, 3491, 3442, 3393, 3344, 3294, 3245, 3196, 3147, 3097, 3048, 2998, 2949, 2900, 2850,
67  2801, 2751, 2701, 2652, 2602, 2553, 2503, 2453, 2404, 2354, 2304, 2254, 2204, 2155, 2105, 2055, 2005, 1955, 1905, 1855, 1805, 1755,
68  1705, 1655, 1605, 1555, 1505, 1455, 1405, 1355, 1305, 1255, 1205, 1155, 1104, 1054, 1004, 954, 904, 854, 803, 753, 703, 653,
69  603, 552, 502, 452, 402, 351, 301, 251, 201, 150, 100, 50, 0, -50, -100, -150, -201, -251, -301, -351, -402, -452,
70  -502, -552, -603, -653, -703, -753, -803, -854, -904, -954, -1004, -1054, -1105, -1155, -1205, -1255, -1305, -1355, -1405, -1455, -1505, -1555,
71  -1605, -1655, -1705, -1755, -1805, -1855, -1905, -1955, -2005, -2055, -2105, -2155, -2204, -2254, -2304, -2354, -2404, -2453, -2503, -2553, -2602, -2652,
72  -2701, -2751, -2801, -2850, -2900, -2949, -2998, -3048, -3097, -3147, -3196, -3245, -3294, -3344, -3393, -3442, -3491, -3540, -3589, -3638, -3687, -3736,
73  -3785, -3834, -3883, -3932, -3980, -4029, -4078, -4127, -4175, -4224, -4272, -4321, -4369, -4418, -4466, -4514, -4563, -4611, -4659, -4707, -4756, -4804,
74  -4852, -4900, -4948, -4995, -5043, -5091, -5139, -5187, -5234, -5282, -5329, -5377, -5424, -5472, -5519, -5566, -5614, -5661, -5708, -5755, -5802, -5849,
75  -5896, -5943, -5990, -6036, -6083, -6130, -6176, -6223, -6269, -6316, -6362, -6408, -6455, -6501, -6547, -6593, -6639, -6685, -6731, -6777, -6822, -6868,
76  -6914, -6959, -7005, -7050, -7095, -7141, -7186, -7231, -7276, -7321, -7366, -7411, -7456, -7500, -7545, -7590, -7634, -7678, -7723, -7767, -7811, -7856,
77  -7900, -7944, -7988, -8031, -8075, -8119, -8162, -8206, -8249, -8293, -8336, -8379, -8423, -8466, -8509, -8552, -8594, -8637, -8680, -8722, -8765, -8807,
78  -8850, -8892, -8934, -8976, -9018, -9060, -9102, -9144, -9185, -9227, -9268, -9310, -9351, -9392, -9434, -9475, -9516, -9556, -9597, -9638, -9679, -9719,
79  -9759, -9800, -9840, -9880, -9920, -9960, -10000, -10040, -10079, -10119, -10159, -10198, -10237, -10276, -10315, -10354, -10393, -10432, -10471, -10510, -10548, -10586,
80  -10625, -10663, -10701, -10739, -10777, -10815, -10853, -10890, -10928, -10965, -11002, -11040, -11077, -11114, -11150, -11187, -11224, -11260, -11297, -11333, -11370, -11406,
81  -11442, -11478, -11513, -11549, -11585, -11620, -11656, -11691, -11726, -11761, -11796, -11831, -11866, -11900, -11935, -11969, -12003, -12037, -12072, -12105, -12139, -12173,
82  -12207, -12240, -12273, -12307, -12340, -12373, -12406, -12438, -12471, -12504, -12536, -12568, -12600, -12633, -12665, -12696, -12728, -12760, -12791, -12822, -12854, -12885,
83  -12916, -12947, -12977, -13008, -13038, -13069, -13099, -13129, -13159, -13189, -13219, -13249, -13278, -13307, -13337, -13366, -13395, -13424, -13452, -13481, -13510, -13538,
84  -13566, -13594, -13622, -13650, -13678, -13705, -13733, -13760, -13788, -13815, -13842, -13868, -13895, -13922, -13948, -13974, -14001, -14027, -14053, -14078, -14104, -14129,
85  -14155, -14180, -14205, -14230, -14255, -14280, -14304, -14329, -14353, -14377, -14401, -14425, -14449, -14473, -14496, -14519, -14543, -14566, -14589, -14611, -14634, -14657,
86  -14679, -14701, -14723, -14745, -14767, -14789, -14810, -14832, -14853, -14874, -14895, -14916, -14937, -14957, -14978, -14998, -15018, -15038, -15058, -15078, -15098, -15117,
87  -15136, -15156, -15175, -15193, -15212, -15231, -15249, -15267, -15286, -15304, -15322, -15339, -15357, -15374, -15392, -15409, -15426, -15443, -15459, -15476, -15492, -15509,
88  -15525, -15541, -15557, -15572, -15588, -15603, -15618, -15634, -15649, -15663, -15678, -15693, -15707, -15721, -15735, -15749, -15763, -15777, -15790, -15803, -15817, -15830,
89  -15842, -15855, -15868, -15880, -15892, -15905, -15917, -15928, -15940, -15952, -15963, -15974, -15985, -15996, -16007, -16018, -16028, -16039, -16049, -16059, -16069, -16078,
90  -16088, -16097, -16107, -16116, -16125, -16134, -16142, -16151, -16159, -16167, -16175, -16183, -16191, -16199, -16206, -16213, -16221, -16228, -16234, -16241, -16248, -16254,
91  -16260, -16266, -16272, -16278, -16284, -16289, -16294, -16300, -16305, -16309, -16314, -16319, -16323, -16327, -16331, -16335, -16339, -16343, -16346, -16350, -16353, -16356,
92  -16359, -16361, -16364, -16366, -16368, -16370, -16372, -16374, -16376, -16377, -16379, -16380, -16381, -16382, -16382, -16383, -16383, -16383, -16383, -16383, -16383, -16383,
93  -16382, -16382, -16381, -16380, -16379, -16377, -16376, -16374, -16372, -16370, -16368, -16366, -16364, -16361, -16359, -16356, -16353, -16350, -16346, -16343, -16339, -16335,
94  -16331, -16327, -16323, -16319, -16314, -16309, -16305, -16300, -16294, -16289, -16284, -16278, -16272, -16266, -16260, -16254, -16248, -16241, -16234, -16228, -16221, -16213,
95  -16206, -16199, -16191, -16183, -16175, -16167, -16159, -16151, -16142, -16134, -16125, -16116, -16107, -16097, -16088, -16078, -16069, -16059, -16049, -16039, -16028, -16018,
96  -16007, -15996, -15985, -15974, -15963, -15952, -15940, -15928, -15917, -15905, -15892, -15880, -15868, -15855, -15842, -15830, -15817, -15803, -15790, -15777, -15763, -15749,
97  -15735, -15721, -15707, -15693, -15678, -15663, -15649, -15634, -15618, -15603, -15588, -15572, -15557, -15541, -15525, -15509, -15492, -15476, -15459, -15443, -15426, -15409,
98  -15392, -15374, -15357, -15339, -15322, -15304, -15286, -15267, -15249, -15231, -15212, -15193, -15175, -15156, -15136, -15117, -15098, -15078, -15058, -15038, -15018, -14998,
99  -14978, -14957, -14937, -14916, -14895, -14874, -14853, -14832, -14810, -14789, -14767, -14745, -14723, -14701, -14679, -14657, -14634, -14611, -14589, -14566, -14543, -14519,
100  -14496, -14473, -14449, -14425, -14401, -14377, -14353, -14329, -14304, -14280, -14255, -14230, -14205, -14180, -14155, -14129, -14104, -14078, -14053, -14027, -14001, -13974,
101  -13948, -13922, -13895, -13868, -13842, -13815, -13788, -13760, -13733, -13705, -13678, -13650, -13622, -13594, -13566, -13538, -13510, -13481, -13452, -13424, -13395, -13366,
102  -13337, -13307, -13278, -13249, -13219, -13189, -13159, -13129, -13099, -13069, -13038, -13008, -12977, -12947, -12916, -12885, -12854, -12822, -12791, -12760, -12728, -12696,
103  -12665, -12633, -12600, -12568, -12536, -12504, -12471, -12438, -12406, -12373, -12340, -12307, -12273, -12240, -12207, -12173, -12139, -12105, -12072, -12037, -12003, -11969,
104  -11935, -11900, -11866, -11831, -11796, -11761, -11726, -11691, -11656, -11620, -11585, -11549, -11513, -11478, -11442, -11406, -11370, -11333, -11297, -11260, -11224, -11187,
105  -11150, -11114, -11077, -11040, -11002, -10965, -10928, -10890, -10853, -10815, -10777, -10739, -10701, -10663, -10625, -10586, -10548, -10510, -10471, -10432, -10393, -10354,
106  -10315, -10276, -10237, -10198, -10159, -10119, -10079, -10040, -10000, -9960, -9920, -9880, -9840, -9800, -9759, -9719, -9679, -9638, -9597, -9556, -9516, -9475,
107  -9434, -9392, -9351, -9310, -9268, -9227, -9185, -9144, -9102, -9060, -9018, -8976, -8934, -8892, -8850, -8807, -8765, -8722, -8680, -8637, -8594, -8552,
108  -8509, -8466, -8423, -8379, -8336, -8293, -8249, -8206, -8162, -8119, -8075, -8031, -7988, -7944, -7900, -7856, -7811, -7767, -7723, -7678, -7634, -7590,
109  -7545, -7500, -7456, -7411, -7366, -7321, -7276, -7231, -7186, -7141, -7095, -7050, -7005, -6959, -6914, -6868, -6822, -6777, -6731, -6685, -6639, -6593,
110  -6547, -6501, -6455, -6408, -6362, -6316, -6269, -6223, -6176, -6130, -6083, -6036, -5990, -5943, -5896, -5849, -5802, -5755, -5708, -5661, -5614, -5566,
111  -5519, -5472, -5424, -5377, -5329, -5282, -5234, -5187, -5139, -5091, -5043, -4995, -4948, -4900, -4852, -4804, -4756, -4707, -4659, -4611, -4563, -4514,
112  -4466, -4418, -4369, -4321, -4272, -4224, -4175, -4127, -4078, -4029, -3980, -3932, -3883, -3834, -3785, -3736, -3687, -3638, -3589, -3540, -3491, -3442,
113  -3393, -3344, -3294, -3245, -3196, -3147, -3097, -3048, -2998, -2949, -2900, -2850, -2801, -2751, -2701, -2652, -2602, -2553, -2503, -2453, -2404, -2354,
114  -2304, -2254, -2204, -2155, -2105, -2055, -2005, -1955, -1905, -1855, -1805, -1755, -1705, -1655, -1605, -1555, -1505, -1455, -1405, -1355, -1305, -1255,
115  -1205, -1155, -1104, -1054, -1004, -954, -904, -854, -803, -753, -703, -653, -603, -552, -502, -452, -402, -351, -301, -251, -201, -150,
116  -100, -50 };
117 
118 const int16_t g_sYICosine[YI_ANGLE2PI] = { 16384, 16383, 16383, 16383, 16382, 16382, 16381, 16380, 16379, 16377, 16376, 16374, 16372, 16370, 16368, 16366, 16364, 16361, 16359, 16356, 16353, 16350,
119  16346, 16343, 16339, 16335, 16331, 16327, 16323, 16319, 16314, 16309, 16305, 16300, 16294, 16289, 16284, 16278, 16272, 16266, 16260, 16254, 16248, 16241,
120  16234, 16228, 16221, 16213, 16206, 16199, 16191, 16183, 16175, 16167, 16159, 16151, 16142, 16134, 16125, 16116, 16107, 16097, 16088, 16078, 16069, 16059,
121  16049, 16039, 16028, 16018, 16007, 15996, 15985, 15974, 15963, 15952, 15940, 15928, 15917, 15905, 15892, 15880, 15868, 15855, 15842, 15830, 15817, 15803,
122  15790, 15777, 15763, 15749, 15735, 15721, 15707, 15693, 15678, 15663, 15649, 15634, 15618, 15603, 15588, 15572, 15557, 15541, 15525, 15509, 15492, 15476,
123  15459, 15443, 15426, 15409, 15392, 15374, 15357, 15339, 15322, 15304, 15286, 15267, 15249, 15231, 15212, 15193, 15175, 15156, 15136, 15117, 15098, 15078,
124  15058, 15038, 15018, 14998, 14978, 14957, 14937, 14916, 14895, 14874, 14853, 14832, 14810, 14789, 14767, 14745, 14723, 14701, 14679, 14657, 14634, 14611,
125  14589, 14566, 14543, 14519, 14496, 14473, 14449, 14425, 14401, 14377, 14353, 14329, 14304, 14280, 14255, 14230, 14205, 14180, 14155, 14129, 14104, 14078,
126  14053, 14027, 14001, 13974, 13948, 13922, 13895, 13868, 13842, 13815, 13788, 13760, 13733, 13705, 13678, 13650, 13622, 13594, 13566, 13538, 13510, 13481,
127  13452, 13424, 13395, 13366, 13337, 13307, 13278, 13249, 13219, 13189, 13159, 13129, 13099, 13069, 13038, 13008, 12977, 12947, 12916, 12885, 12854, 12822,
128  12791, 12760, 12728, 12696, 12665, 12633, 12600, 12568, 12536, 12504, 12471, 12438, 12406, 12373, 12340, 12307, 12273, 12240, 12207, 12173, 12139, 12105,
129  12072, 12037, 12003, 11969, 11935, 11900, 11866, 11831, 11796, 11761, 11726, 11691, 11656, 11620, 11585, 11549, 11513, 11478, 11442, 11406, 11370, 11333,
130  11297, 11260, 11224, 11187, 11150, 11114, 11077, 11040, 11002, 10965, 10928, 10890, 10853, 10815, 10777, 10739, 10701, 10663, 10625, 10586, 10548, 10510,
131  10471, 10432, 10393, 10354, 10315, 10276, 10237, 10198, 10159, 10119, 10079, 10040, 10000, 9960, 9920, 9880, 9840, 9800, 9759, 9719, 9679, 9638,
132  9597, 9556, 9516, 9475, 9434, 9392, 9351, 9310, 9268, 9227, 9185, 9144, 9102, 9060, 9018, 8976, 8934, 8892, 8850, 8807, 8765, 8722,
133  8680, 8637, 8594, 8552, 8509, 8466, 8423, 8379, 8336, 8293, 8249, 8206, 8162, 8119, 8075, 8031, 7988, 7944, 7900, 7856, 7811, 7767,
134  7723, 7678, 7634, 7590, 7545, 7500, 7456, 7411, 7366, 7321, 7276, 7231, 7186, 7141, 7095, 7050, 7005, 6959, 6914, 6868, 6822, 6777,
135  6731, 6685, 6639, 6593, 6547, 6501, 6455, 6408, 6362, 6316, 6269, 6223, 6176, 6130, 6083, 6036, 5990, 5943, 5896, 5849, 5802, 5755,
136  5708, 5661, 5614, 5566, 5519, 5472, 5424, 5377, 5329, 5282, 5234, 5187, 5139, 5091, 5043, 4995, 4948, 4900, 4852, 4804, 4756, 4707,
137  4659, 4611, 4563, 4514, 4466, 4418, 4369, 4321, 4272, 4224, 4175, 4127, 4078, 4029, 3980, 3932, 3883, 3834, 3785, 3736, 3687, 3638,
138  3589, 3540, 3491, 3442, 3393, 3344, 3294, 3245, 3196, 3147, 3097, 3048, 2998, 2949, 2900, 2850, 2801, 2751, 2701, 2652, 2602, 2553,
139  2503, 2453, 2404, 2354, 2304, 2254, 2204, 2155, 2105, 2055, 2005, 1955, 1905, 1855, 1805, 1755, 1705, 1655, 1605, 1555, 1505, 1455,
140  1405, 1355, 1305, 1255, 1205, 1155, 1105, 1054, 1004, 954, 904, 854, 803, 753, 703, 653, 603, 552, 502, 452, 402, 351,
141  301, 251, 201, 150, 100, 50, 0, -50, -100, -150, -201, -251, -301, -351, -402, -452, -502, -552, -603, -653, -703, -753,
142  -803, -854, -904, -954, -1004, -1054, -1105, -1155, -1205, -1255, -1305, -1355, -1405, -1455, -1505, -1555, -1605, -1655, -1705, -1755, -1805, -1855,
143  -1905, -1955, -2005, -2055, -2105, -2155, -2204, -2254, -2304, -2354, -2404, -2453, -2503, -2553, -2602, -2652, -2701, -2751, -2801, -2850, -2900, -2949,
144  -2998, -3048, -3097, -3147, -3196, -3245, -3294, -3344, -3393, -3442, -3491, -3540, -3589, -3638, -3687, -3736, -3785, -3834, -3883, -3932, -3980, -4029,
145  -4078, -4127, -4175, -4224, -4272, -4321, -4369, -4418, -4466, -4514, -4563, -4611, -4659, -4707, -4756, -4804, -4852, -4900, -4948, -4995, -5043, -5091,
146  -5139, -5187, -5234, -5282, -5329, -5377, -5424, -5472, -5519, -5566, -5614, -5661, -5708, -5755, -5802, -5849, -5896, -5943, -5990, -6036, -6083, -6130,
147  -6176, -6223, -6269, -6316, -6362, -6408, -6455, -6501, -6547, -6593, -6639, -6685, -6731, -6777, -6822, -6868, -6914, -6959, -7005, -7050, -7095, -7141,
148  -7186, -7231, -7276, -7321, -7366, -7411, -7456, -7500, -7545, -7590, -7634, -7678, -7723, -7767, -7811, -7856, -7900, -7944, -7988, -8031, -8075, -8119,
149  -8162, -8206, -8249, -8293, -8336, -8379, -8423, -8466, -8509, -8552, -8594, -8637, -8680, -8722, -8765, -8807, -8850, -8892, -8934, -8976, -9018, -9060,
150  -9102, -9144, -9185, -9227, -9268, -9310, -9351, -9392, -9434, -9475, -9516, -9556, -9597, -9638, -9679, -9719, -9759, -9800, -9840, -9880, -9920, -9960,
151  -10000, -10040, -10079, -10119, -10159, -10198, -10237, -10276, -10315, -10354, -10393, -10432, -10471, -10510, -10548, -10586, -10625, -10663, -10701, -10739, -10777, -10815,
152  -10853, -10890, -10928, -10965, -11002, -11040, -11077, -11114, -11150, -11187, -11224, -11260, -11297, -11333, -11370, -11406, -11442, -11478, -11513, -11549, -11585, -11620,
153  -11656, -11691, -11726, -11761, -11796, -11831, -11866, -11900, -11935, -11969, -12003, -12037, -12072, -12105, -12139, -12173, -12207, -12240, -12273, -12307, -12340, -12373,
154  -12406, -12438, -12471, -12504, -12536, -12568, -12600, -12633, -12665, -12696, -12728, -12760, -12791, -12822, -12854, -12885, -12916, -12947, -12977, -13008, -13038, -13069,
155  -13099, -13129, -13159, -13189, -13219, -13249, -13278, -13307, -13337, -13366, -13395, -13424, -13452, -13481, -13510, -13538, -13566, -13594, -13622, -13650, -13678, -13705,
156  -13733, -13760, -13788, -13815, -13842, -13868, -13895, -13922, -13948, -13974, -14001, -14027, -14053, -14078, -14104, -14129, -14155, -14180, -14205, -14230, -14255, -14280,
157  -14304, -14329, -14353, -14377, -14401, -14425, -14449, -14473, -14496, -14519, -14543, -14566, -14589, -14611, -14634, -14657, -14679, -14701, -14723, -14745, -14767, -14789,
158  -14810, -14832, -14853, -14874, -14895, -14916, -14937, -14957, -14978, -14998, -15018, -15038, -15058, -15078, -15098, -15117, -15136, -15156, -15175, -15193, -15212, -15231,
159  -15249, -15267, -15286, -15304, -15322, -15339, -15357, -15374, -15392, -15409, -15426, -15443, -15459, -15476, -15492, -15509, -15525, -15541, -15557, -15572, -15588, -15603,
160  -15618, -15634, -15649, -15663, -15678, -15693, -15707, -15721, -15735, -15749, -15763, -15777, -15790, -15803, -15817, -15830, -15842, -15855, -15868, -15880, -15892, -15905,
161  -15917, -15928, -15940, -15952, -15963, -15974, -15985, -15996, -16007, -16018, -16028, -16039, -16049, -16059, -16069, -16078, -16088, -16097, -16107, -16116, -16125, -16134,
162  -16142, -16151, -16159, -16167, -16175, -16183, -16191, -16199, -16206, -16213, -16221, -16228, -16234, -16241, -16248, -16254, -16260, -16266, -16272, -16278, -16284, -16289,
163  -16294, -16300, -16305, -16309, -16314, -16319, -16323, -16327, -16331, -16335, -16339, -16343, -16346, -16350, -16353, -16356, -16359, -16361, -16364, -16366, -16368, -16370,
164  -16372, -16374, -16376, -16377, -16379, -16380, -16381, -16382, -16382, -16383, -16383, -16383, -16383, -16383, -16383, -16383, -16382, -16382, -16381, -16380, -16379, -16377,
165  -16376, -16374, -16372, -16370, -16368, -16366, -16364, -16361, -16359, -16356, -16353, -16350, -16346, -16343, -16339, -16335, -16331, -16327, -16323, -16319, -16314, -16309,
166  -16305, -16300, -16294, -16289, -16284, -16278, -16272, -16266, -16260, -16254, -16248, -16241, -16234, -16228, -16221, -16213, -16206, -16199, -16191, -16183, -16175, -16167,
167  -16159, -16151, -16142, -16134, -16125, -16116, -16107, -16097, -16088, -16078, -16069, -16059, -16049, -16039, -16028, -16018, -16007, -15996, -15985, -15974, -15963, -15952,
168  -15940, -15928, -15917, -15905, -15892, -15880, -15868, -15855, -15842, -15830, -15817, -15803, -15790, -15777, -15763, -15749, -15735, -15721, -15707, -15693, -15678, -15663,
169  -15649, -15634, -15618, -15603, -15588, -15572, -15557, -15541, -15525, -15509, -15492, -15476, -15459, -15443, -15426, -15409, -15392, -15374, -15357, -15339, -15322, -15304,
170  -15286, -15267, -15249, -15231, -15212, -15193, -15175, -15156, -15136, -15117, -15098, -15078, -15058, -15038, -15018, -14998, -14978, -14957, -14937, -14916, -14895, -14874,
171  -14853, -14832, -14810, -14789, -14767, -14745, -14723, -14701, -14679, -14657, -14634, -14611, -14589, -14566, -14543, -14519, -14496, -14473, -14449, -14425, -14401, -14377,
172  -14353, -14329, -14304, -14280, -14255, -14230, -14205, -14180, -14155, -14129, -14104, -14078, -14053, -14027, -14001, -13974, -13948, -13922, -13895, -13868, -13842, -13815,
173  -13788, -13760, -13733, -13705, -13678, -13650, -13622, -13594, -13566, -13538, -13510, -13481, -13452, -13424, -13395, -13366, -13337, -13307, -13278, -13249, -13219, -13189,
174  -13159, -13129, -13099, -13069, -13038, -13008, -12977, -12947, -12916, -12885, -12854, -12822, -12791, -12760, -12728, -12696, -12665, -12633, -12600, -12568, -12536, -12504,
175  -12471, -12438, -12406, -12373, -12340, -12307, -12273, -12240, -12207, -12173, -12139, -12105, -12072, -12037, -12003, -11969, -11935, -11900, -11866, -11831, -11796, -11761,
176  -11726, -11691, -11656, -11620, -11585, -11549, -11513, -11478, -11442, -11406, -11370, -11333, -11297, -11260, -11224, -11187, -11150, -11114, -11077, -11040, -11002, -10965,
177  -10928, -10890, -10853, -10815, -10777, -10739, -10701, -10663, -10625, -10586, -10548, -10510, -10471, -10432, -10393, -10354, -10315, -10276, -10237, -10198, -10159, -10119,
178  -10079, -10040, -10000, -9960, -9920, -9880, -9840, -9800, -9759, -9719, -9679, -9638, -9597, -9556, -9516, -9475, -9434, -9392, -9351, -9310, -9268, -9227,
179  -9185, -9144, -9102, -9060, -9018, -8976, -8934, -8892, -8850, -8807, -8765, -8722, -8680, -8637, -8594, -8552, -8509, -8466, -8423, -8379, -8336, -8293,
180  -8249, -8206, -8162, -8119, -8075, -8031, -7988, -7944, -7900, -7856, -7811, -7767, -7723, -7678, -7634, -7590, -7545, -7500, -7456, -7411, -7366, -7321,
181  -7276, -7231, -7186, -7141, -7095, -7050, -7005, -6959, -6914, -6868, -6822, -6777, -6731, -6685, -6639, -6593, -6547, -6501, -6455, -6408, -6362, -6316,
182  -6269, -6223, -6176, -6130, -6083, -6036, -5990, -5943, -5896, -5849, -5802, -5755, -5708, -5661, -5614, -5566, -5519, -5472, -5424, -5377, -5329, -5282,
183  -5234, -5187, -5139, -5091, -5043, -4995, -4948, -4900, -4852, -4804, -4756, -4707, -4659, -4611, -4563, -4514, -4466, -4418, -4369, -4321, -4272, -4224,
184  -4175, -4127, -4078, -4029, -3980, -3932, -3883, -3834, -3785, -3736, -3687, -3638, -3589, -3540, -3491, -3442, -3393, -3344, -3294, -3245, -3196, -3147,
185  -3097, -3048, -2998, -2949, -2900, -2850, -2801, -2751, -2701, -2652, -2602, -2553, -2503, -2453, -2404, -2354, -2304, -2254, -2204, -2155, -2105, -2055,
186  -2005, -1955, -1905, -1855, -1805, -1755, -1705, -1655, -1605, -1555, -1505, -1455, -1405, -1355, -1305, -1255, -1205, -1155, -1104, -1054, -1004, -954,
187  -904, -854, -803, -753, -703, -653, -603, -552, -502, -452, -402, -351, -301, -251, -201, -150, -100, -50, 0, 50, 100, 150,
188  201, 251, 301, 351, 402, 452, 502, 552, 603, 653, 703, 753, 803, 854, 904, 954, 1004, 1054, 1105, 1155, 1205, 1255,
189  1305, 1355, 1405, 1455, 1505, 1555, 1605, 1655, 1705, 1755, 1805, 1855, 1905, 1955, 2005, 2055, 2105, 2155, 2204, 2254, 2304, 2354,
190  2404, 2453, 2503, 2553, 2602, 2652, 2701, 2751, 2801, 2850, 2900, 2949, 2998, 3048, 3097, 3147, 3196, 3245, 3294, 3344, 3393, 3442,
191  3491, 3540, 3589, 3638, 3687, 3736, 3785, 3834, 3883, 3932, 3980, 4029, 4078, 4127, 4175, 4224, 4272, 4321, 4369, 4418, 4466, 4514,
192  4563, 4611, 4659, 4707, 4756, 4804, 4852, 4900, 4948, 4995, 5043, 5091, 5139, 5187, 5234, 5282, 5329, 5377, 5424, 5472, 5519, 5566,
193  5614, 5661, 5708, 5755, 5802, 5849, 5896, 5943, 5990, 6036, 6083, 6130, 6176, 6223, 6269, 6316, 6362, 6408, 6455, 6501, 6547, 6593,
194  6639, 6685, 6731, 6777, 6822, 6868, 6914, 6959, 7005, 7050, 7095, 7141, 7186, 7231, 7276, 7321, 7366, 7411, 7456, 7500, 7545, 7590,
195  7634, 7678, 7723, 7767, 7811, 7856, 7900, 7944, 7988, 8031, 8075, 8119, 8162, 8206, 8249, 8293, 8336, 8379, 8423, 8466, 8509, 8552,
196  8594, 8637, 8680, 8722, 8765, 8807, 8850, 8892, 8934, 8976, 9018, 9060, 9102, 9144, 9185, 9227, 9268, 9310, 9351, 9392, 9434, 9475,
197  9516, 9556, 9597, 9638, 9679, 9719, 9759, 9800, 9840, 9880, 9920, 9960, 10000, 10040, 10079, 10119, 10159, 10198, 10237, 10276, 10315, 10354,
198  10393, 10432, 10471, 10510, 10548, 10586, 10625, 10663, 10701, 10739, 10777, 10815, 10853, 10890, 10928, 10965, 11002, 11040, 11077, 11114, 11150, 11187,
199  11224, 11260, 11297, 11333, 11370, 11406, 11442, 11478, 11513, 11549, 11585, 11620, 11656, 11691, 11726, 11761, 11796, 11831, 11866, 11900, 11935, 11969,
200  12003, 12037, 12072, 12105, 12139, 12173, 12207, 12240, 12273, 12307, 12340, 12373, 12406, 12438, 12471, 12504, 12536, 12568, 12600, 12633, 12665, 12696,
201  12728, 12760, 12791, 12822, 12854, 12885, 12916, 12947, 12977, 13008, 13038, 13069, 13099, 13129, 13159, 13189, 13219, 13249, 13278, 13307, 13337, 13366,
202  13395, 13424, 13452, 13481, 13510, 13538, 13566, 13594, 13622, 13650, 13678, 13705, 13733, 13760, 13788, 13815, 13842, 13868, 13895, 13922, 13948, 13974,
203  14001, 14027, 14053, 14078, 14104, 14129, 14155, 14180, 14205, 14230, 14255, 14280, 14304, 14329, 14353, 14377, 14401, 14425, 14449, 14473, 14496, 14519,
204  14543, 14566, 14589, 14611, 14634, 14657, 14679, 14701, 14723, 14745, 14767, 14789, 14810, 14832, 14853, 14874, 14895, 14916, 14937, 14957, 14978, 14998,
205  15018, 15038, 15058, 15078, 15098, 15117, 15136, 15156, 15175, 15193, 15212, 15231, 15249, 15267, 15286, 15304, 15322, 15339, 15357, 15374, 15392, 15409,
206  15426, 15443, 15459, 15476, 15492, 15509, 15525, 15541, 15557, 15572, 15588, 15603, 15618, 15634, 15649, 15663, 15678, 15693, 15707, 15721, 15735, 15749,
207  15763, 15777, 15790, 15803, 15817, 15830, 15842, 15855, 15868, 15880, 15892, 15905, 15917, 15928, 15940, 15952, 15963, 15974, 15985, 15996, 16007, 16018,
208  16028, 16039, 16049, 16059, 16069, 16078, 16088, 16097, 16107, 16116, 16125, 16134, 16142, 16151, 16159, 16167, 16175, 16183, 16191, 16199, 16206, 16213,
209  16221, 16228, 16234, 16241, 16248, 16254, 16260, 16266, 16272, 16278, 16284, 16289, 16294, 16300, 16305, 16309, 16314, 16319, 16323, 16327, 16331, 16335,
210  16339, 16343, 16346, 16350, 16353, 16356, 16359, 16361, 16364, 16366, 16368, 16370, 16372, 16374, 16376, 16377, 16379, 16380, 16381, 16382, 16382, 16383,
211  16383, 16383 };
212 
213 const uint16_t g_usYIArctan[YI_ATAN_SIZE + 1] = { 0, 0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12, 12, 13,
214  13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27,
215  27, 28, 29, 29, 30, 31, 31, 32, 32, 33, 34, 34, 35, 36, 36, 37, 38, 38, 39, 39, 40, 41,
216  41, 42, 43, 43, 44, 44, 45, 46, 46, 47, 48, 48, 49, 49, 50, 51, 51, 52, 53, 53, 54, 54,
217  55, 56, 56, 57, 57, 58, 59, 59, 60, 61, 61, 62, 62, 63, 64, 64, 65, 65, 66, 67, 67, 68,
218  68, 69, 70, 70, 71, 72, 72, 73, 73, 74, 75, 75, 76, 76, 77, 78, 78, 79, 79, 80, 81, 81,
219  82, 82, 83, 84, 84, 85, 85, 86, 87, 87, 88, 88, 89, 89, 90, 91, 91, 92, 92, 93, 94, 94,
220  95, 95, 96, 96, 97, 98, 98, 99, 99, 100, 101, 101, 102, 102, 103, 103, 104, 105, 105, 106, 106, 107,
221  107, 108, 109, 109, 110, 110, 111, 111, 112, 113, 113, 114, 114, 115, 115, 116, 116, 117, 118, 118, 119, 119,
222  120, 120, 121, 121, 122, 123, 123, 124, 124, 125, 125, 126, 126, 127, 127, 128, 129, 129, 130, 130, 131, 131,
223  132, 132, 133, 133, 134, 134, 135, 136, 136, 137, 137, 138, 138, 139, 139, 140, 140, 141, 141, 142, 142, 143,
224  143, 144, 144, 145, 145, 146, 147, 147, 148, 148, 149, 149, 150, 150, 151, 151, 152, 152, 153, 153, 154, 154,
225  155, 155, 156, 156, 157, 157, 158, 158, 159, 159, 160, 160, 161, 161, 162, 162, 163, 163, 164, 164, 165, 165,
226  166, 166, 167, 167, 167, 168, 168, 169, 169, 170, 170, 171, 171, 172, 172, 173, 173, 174, 174, 175, 175, 176,
227  176, 176, 177, 177, 178, 178, 179, 179, 180, 180, 181, 181, 182, 182, 182, 183, 183, 184, 184, 185, 185, 186,
228  186, 187, 187, 187, 188, 188, 189, 189, 190, 190, 191, 191, 191, 192, 192, 193, 193, 194, 194, 195, 195, 195,
229  196, 196, 197, 197, 198, 198, 198, 199, 199, 200, 200, 201, 201, 201, 202, 202, 203, 203, 203, 204, 204, 205,
230  205, 206, 206, 206, 207, 207, 208, 208, 208, 209, 209, 210, 210, 210, 211, 211, 212, 212, 212, 213, 213, 214,
231  214, 214, 215, 215, 216, 216, 216, 217, 217, 218, 218, 218, 219, 219, 220, 220, 220, 221, 221, 222, 222, 222,
232  223, 223, 223, 224, 224, 225, 225, 225, 226, 226, 226, 227, 227, 228, 228, 228, 229, 229, 229, 230, 230, 231,
233  231, 231, 232, 232, 232, 233, 233, 233, 234, 234, 235, 235, 235, 236, 236, 236, 237, 237, 237, 238, 238, 238,
234  239, 239, 239, 240, 240, 241, 241, 241, 242, 242, 242, 243, 243, 243, 244, 244, 244, 245, 245, 245, 246, 246,
235  246, 247, 247, 247, 248, 248, 248, 249, 249, 249, 250, 250, 250, 251, 251, 251, 252, 252, 252, 253, 253, 253,
236  254, 254, 254, 255, 255, 255, 255 };
237 
238 const uint16_t g_usYISqrt[4096] = { 0, 1024, 1448, 1773, 2048, 2289, 2508, 2709, 2896, 3072, 3238, 3396, 3547, 3692, 3831, 3965, 4096, 4222, 4344, 4463, 4579, 4692,
239  4802, 4910, 5016, 5120, 5221, 5320, 5418, 5514, 5608, 5701, 5792, 5882, 5970, 6058, 6144, 6228, 6312, 6394, 6476, 6556, 6636, 6714,
240  6792, 6869, 6945, 7020, 7094, 7168, 7240, 7312, 7384, 7454, 7524, 7594, 7662, 7731, 7798, 7865, 7931, 7997, 8062, 8127, 8192, 8255,
241  8319, 8381, 8444, 8505, 8567, 8628, 8688, 8749, 8808, 8868, 8927, 8985, 9043, 9101, 9158, 9216, 9272, 9329, 9385, 9440, 9496, 9551,
242  9605, 9660, 9714, 9768, 9821, 9875, 9928, 9980, 10033, 10085, 10137, 10188, 10240, 10291, 10341, 10392, 10442, 10492, 10542, 10592, 10641, 10690,
243  10739, 10788, 10836, 10885, 10933, 10981, 11028, 11076, 11123, 11170, 11217, 11264, 11310, 11356, 11402, 11448, 11494, 11539, 11585, 11630, 11675, 11720,
244  11764, 11809, 11853, 11897, 11941, 11985, 12029, 12072, 12116, 12159, 12202, 12245, 12288, 12330, 12373, 12415, 12457, 12499, 12541, 12583, 12624, 12666,
245  12707, 12748, 12789, 12830, 12871, 12912, 12952, 12993, 13033, 13073, 13113, 13153, 13193, 13232, 13272, 13312, 13351, 13390, 13429, 13468, 13507, 13546,
246  13584, 13623, 13661, 13700, 13738, 13776, 13814, 13852, 13890, 13927, 13965, 14002, 14040, 14077, 14114, 14151, 14188, 14225, 14262, 14299, 14336, 14372,
247  14408, 14445, 14481, 14517, 14553, 14589, 14625, 14661, 14697, 14732, 14768, 14803, 14839, 14874, 14909, 14944, 14979, 15014, 15049, 15084, 15119, 15153,
248  15188, 15222, 15257, 15291, 15325, 15360, 15394, 15428, 15462, 15495, 15529, 15563, 15597, 15630, 15664, 15697, 15730, 15764, 15797, 15830, 15863, 15896,
249  15929, 15962, 15995, 16028, 16060, 16093, 16125, 16158, 16190, 16223, 16255, 16287, 16319, 16351, 16384, 16415, 16447, 16479, 16511, 16543, 16574, 16606,
250  16638, 16669, 16700, 16732, 16763, 16794, 16826, 16857, 16888, 16919, 16950, 16981, 17011, 17042, 17073, 17104, 17134, 17165, 17195, 17226, 17256, 17287,
251  17317, 17347, 17377, 17408, 17438, 17468, 17498, 17528, 17557, 17587, 17617, 17647, 17676, 17706, 17736, 17765, 17795, 17824, 17854, 17883, 17912, 17941,
252  17971, 18000, 18029, 18058, 18087, 18116, 18145, 18174, 18203, 18231, 18260, 18289, 18317, 18346, 18375, 18403, 18432, 18460, 18488, 18517, 18545, 18573,
253  18601, 18630, 18658, 18686, 18714, 18742, 18770, 18798, 18826, 18853, 18881, 18909, 18937, 18964, 18992, 19019, 19047, 19075, 19102, 19129, 19157, 19184,
254  19211, 19239, 19266, 19293, 19320, 19347, 19374, 19402, 19429, 19456, 19482, 19509, 19536, 19563, 19590, 19617, 19643, 19670, 19697, 19723, 19750, 19776,
255  19803, 19829, 19856, 19882, 19908, 19935, 19961, 19987, 20013, 20040, 20066, 20092, 20118, 20144, 20170, 20196, 20222, 20248, 20274, 20300, 20325, 20351,
256  20377, 20403, 20428, 20454, 20480, 20505, 20531, 20556, 20582, 20607, 20633, 20658, 20683, 20709, 20734, 20759, 20784, 20810, 20835, 20860, 20885, 20910,
257  20935, 20960, 20985, 21010, 21035, 21060, 21085, 21110, 21135, 21159, 21184, 21209, 21234, 21258, 21283, 21308, 21332, 21357, 21381, 21406, 21430, 21455,
258  21479, 21504, 21528, 21552, 21577, 21601, 21625, 21649, 21673, 21698, 21722, 21746, 21770, 21794, 21818, 21842, 21866, 21890, 21914, 21938, 21962, 21986,
259  22010, 22033, 22057, 22081, 22105, 22128, 22152, 22176, 22199, 22223, 22246, 22270, 22294, 22317, 22341, 22364, 22387, 22411, 22434, 22458, 22481, 22504,
260  22528, 22551, 22574, 22597, 22620, 22644, 22667, 22690, 22713, 22736, 22759, 22782, 22805, 22828, 22851, 22874, 22897, 22920, 22943, 22965, 22988, 23011,
261  23034, 23057, 23079, 23102, 23125, 23147, 23170, 23193, 23215, 23238, 23260, 23283, 23305, 23328, 23350, 23373, 23395, 23418, 23440, 23462, 23485, 23507,
262  23529, 23552, 23574, 23596, 23618, 23640, 23663, 23685, 23707, 23729, 23751, 23773, 23795, 23817, 23839, 23861, 23883, 23905, 23927, 23949, 23971, 23993,
263  24014, 24036, 24058, 24080, 24102, 24123, 24145, 24167, 24188, 24210, 24232, 24253, 24275, 24297, 24318, 24340, 24361, 24383, 24404, 24426, 24447, 24469,
264  24490, 24511, 24533, 24554, 24576, 24597, 24618, 24639, 24661, 24682, 24703, 24724, 24746, 24767, 24788, 24809, 24830, 24851, 24872, 24893, 24914, 24936,
265  24957, 24978, 24999, 25019, 25040, 25061, 25082, 25103, 25124, 25145, 25166, 25187, 25207, 25228, 25249, 25270, 25290, 25311, 25332, 25353, 25373, 25394,
266  25415, 25435, 25456, 25476, 25497, 25517, 25538, 25559, 25579, 25600, 25620, 25640, 25661, 25681, 25702, 25722, 25742, 25763, 25783, 25803, 25824, 25844,
267  25864, 25885, 25905, 25925, 25945, 25966, 25986, 26006, 26026, 26046, 26066, 26086, 26106, 26127, 26147, 26167, 26187, 26207, 26227, 26247, 26267, 26287,
268  26307, 26326, 26346, 26366, 26386, 26406, 26426, 26446, 26465, 26485, 26505, 26525, 26545, 26564, 26584, 26604, 26624, 26643, 26663, 26683, 26702, 26722,
269  26741, 26761, 26781, 26800, 26820, 26839, 26859, 26878, 26898, 26917, 26937, 26956, 26976, 26995, 27014, 27034, 27053, 27073, 27092, 27111, 27131, 27150,
270  27169, 27189, 27208, 27227, 27246, 27266, 27285, 27304, 27323, 27342, 27362, 27381, 27400, 27419, 27438, 27457, 27476, 27495, 27514, 27533, 27553, 27572,
271  27591, 27610, 27629, 27648, 27666, 27685, 27704, 27723, 27742, 27761, 27780, 27799, 27818, 27836, 27855, 27874, 27893, 27912, 27930, 27949, 27968, 27987,
272  28005, 28024, 28043, 28062, 28080, 28099, 28118, 28136, 28155, 28173, 28192, 28211, 28229, 28248, 28266, 28285, 28303, 28322, 28340, 28359, 28377, 28396,
273  28414, 28433, 28451, 28470, 28488, 28506, 28525, 28543, 28562, 28580, 28598, 28617, 28635, 28653, 28672, 28690, 28708, 28726, 28745, 28763, 28781, 28799,
274  28817, 28836, 28854, 28872, 28890, 28908, 28926, 28944, 28963, 28981, 28999, 29017, 29035, 29053, 29071, 29089, 29107, 29125, 29143, 29161, 29179, 29197,
275  29215, 29233, 29251, 29269, 29287, 29305, 29322, 29340, 29358, 29376, 29394, 29412, 29429, 29447, 29465, 29483, 29501, 29518, 29536, 29554, 29572, 29589,
276  29607, 29625, 29642, 29660, 29678, 29696, 29713, 29731, 29748, 29766, 29784, 29801, 29819, 29836, 29854, 29872, 29889, 29907, 29924, 29942, 29959, 29977,
277  29994, 30012, 30029, 30047, 30064, 30081, 30099, 30116, 30134, 30151, 30168, 30186, 30203, 30221, 30238, 30255, 30273, 30290, 30307, 30324, 30342, 30359,
278  30376, 30394, 30411, 30428, 30445, 30462, 30480, 30497, 30514, 30531, 30548, 30566, 30583, 30600, 30617, 30634, 30651, 30668, 30685, 30702, 30720, 30737,
279  30754, 30771, 30788, 30805, 30822, 30839, 30856, 30873, 30890, 30907, 30924, 30941, 30958, 30974, 30991, 31008, 31025, 31042, 31059, 31076, 31093, 31110,
280  31126, 31143, 31160, 31177, 31194, 31211, 31227, 31244, 31261, 31278, 31294, 31311, 31328, 31345, 31361, 31378, 31395, 31411, 31428, 31445, 31461, 31478,
281  31495, 31511, 31528, 31545, 31561, 31578, 31595, 31611, 31628, 31644, 31661, 31677, 31694, 31710, 31727, 31744, 31760, 31777, 31793, 31809, 31826, 31842,
282  31859, 31875, 31892, 31908, 31925, 31941, 31957, 31974, 31990, 32007, 32023, 32039, 32056, 32072, 32088, 32105, 32121, 32137, 32154, 32170, 32186, 32203,
283  32219, 32235, 32251, 32268, 32284, 32300, 32316, 32333, 32349, 32365, 32381, 32397, 32414, 32430, 32446, 32462, 32478, 32494, 32510, 32527, 32543, 32559,
284  32575, 32591, 32607, 32623, 32639, 32655, 32671, 32687, 32703, 32719, 32735, 32751, 32768, 32783, 32799, 32815, 32831, 32847, 32863, 32879, 32895, 32911,
285  32927, 32943, 32959, 32975, 32991, 33007, 33023, 33038, 33054, 33070, 33086, 33102, 33118, 33133, 33149, 33165, 33181, 33197, 33212, 33228, 33244, 33260,
286  33276, 33291, 33307, 33323, 33339, 33354, 33370, 33386, 33401, 33417, 33433, 33448, 33464, 33480, 33495, 33511, 33527, 33542, 33558, 33574, 33589, 33605,
287  33620, 33636, 33652, 33667, 33683, 33698, 33714, 33729, 33745, 33760, 33776, 33792, 33807, 33823, 33838, 33854, 33869, 33884, 33900, 33915, 33931, 33946,
288  33962, 33977, 33993, 34008, 34023, 34039, 34054, 34070, 34085, 34100, 34116, 34131, 34146, 34162, 34177, 34193, 34208, 34223, 34238, 34254, 34269, 34284,
289  34300, 34315, 34330, 34346, 34361, 34376, 34391, 34407, 34422, 34437, 34452, 34467, 34483, 34498, 34513, 34528, 34543, 34559, 34574, 34589, 34604, 34619,
290  34634, 34649, 34665, 34680, 34695, 34710, 34725, 34740, 34755, 34770, 34785, 34800, 34816, 34831, 34846, 34861, 34876, 34891, 34906, 34921, 34936, 34951,
291  34966, 34981, 34996, 35011, 35026, 35041, 35056, 35071, 35086, 35100, 35115, 35130, 35145, 35160, 35175, 35190, 35205, 35220, 35235, 35250, 35264, 35279,
292  35294, 35309, 35324, 35339, 35353, 35368, 35383, 35398, 35413, 35428, 35442, 35457, 35472, 35487, 35501, 35516, 35531, 35546, 35560, 35575, 35590, 35605,
293  35619, 35634, 35649, 35664, 35678, 35693, 35708, 35722, 35737, 35752, 35766, 35781, 35796, 35810, 35825, 35840, 35854, 35869, 35883, 35898, 35913, 35927,
294  35942, 35956, 35971, 35985, 36000, 36015, 36029, 36044, 36058, 36073, 36087, 36102, 36116, 36131, 36145, 36160, 36174, 36189, 36203, 36218, 36232, 36247,
295  36261, 36276, 36290, 36305, 36319, 36333, 36348, 36362, 36377, 36391, 36406, 36420, 36434, 36449, 36463, 36477, 36492, 36506, 36521, 36535, 36549, 36564,
296  36578, 36592, 36607, 36621, 36635, 36650, 36664, 36678, 36692, 36707, 36721, 36735, 36750, 36764, 36778, 36792, 36807, 36821, 36835, 36849, 36864, 36878,
297  36892, 36906, 36920, 36935, 36949, 36963, 36977, 36991, 37005, 37020, 37034, 37048, 37062, 37076, 37090, 37104, 37119, 37133, 37147, 37161, 37175, 37189,
298  37203, 37217, 37231, 37246, 37260, 37274, 37288, 37302, 37316, 37330, 37344, 37358, 37372, 37386, 37400, 37414, 37428, 37442, 37456, 37470, 37484, 37498,
299  37512, 37526, 37540, 37554, 37568, 37582, 37596, 37610, 37624, 37638, 37652, 37665, 37679, 37693, 37707, 37721, 37735, 37749, 37763, 37777, 37791, 37804,
300  37818, 37832, 37846, 37860, 37874, 37888, 37901, 37915, 37929, 37943, 37957, 37970, 37984, 37998, 38012, 38026, 38039, 38053, 38067, 38081, 38095, 38108,
301  38122, 38136, 38150, 38163, 38177, 38191, 38204, 38218, 38232, 38246, 38259, 38273, 38287, 38300, 38314, 38328, 38341, 38355, 38369, 38382, 38396, 38410,
302  38423, 38437, 38451, 38464, 38478, 38492, 38505, 38519, 38532, 38546, 38560, 38573, 38587, 38600, 38614, 38628, 38641, 38655, 38668, 38682, 38695, 38709,
303  38722, 38736, 38749, 38763, 38777, 38790, 38804, 38817, 38831, 38844, 38858, 38871, 38885, 38898, 38912, 38925, 38938, 38952, 38965, 38979, 38992, 39006,
304  39019, 39033, 39046, 39059, 39073, 39086, 39100, 39113, 39126, 39140, 39153, 39167, 39180, 39193, 39207, 39220, 39234, 39247, 39260, 39274, 39287, 39300,
305  39314, 39327, 39340, 39354, 39367, 39380, 39394, 39407, 39420, 39433, 39447, 39460, 39473, 39487, 39500, 39513, 39526, 39540, 39553, 39566, 39579, 39593,
306  39606, 39619, 39632, 39646, 39659, 39672, 39685, 39698, 39712, 39725, 39738, 39751, 39764, 39778, 39791, 39804, 39817, 39830, 39843, 39857, 39870, 39883,
307  39896, 39909, 39922, 39936, 39949, 39962, 39975, 39988, 40001, 40014, 40027, 40040, 40053, 40067, 40080, 40093, 40106, 40119, 40132, 40145, 40158, 40171,
308  40184, 40197, 40210, 40223, 40236, 40249, 40262, 40275, 40288, 40301, 40314, 40327, 40340, 40353, 40366, 40379, 40392, 40405, 40418, 40431, 40444, 40457,
309  40470, 40483, 40496, 40509, 40522, 40535, 40548, 40561, 40574, 40587, 40600, 40612, 40625, 40638, 40651, 40664, 40677, 40690, 40703, 40716, 40728, 40741,
310  40754, 40767, 40780, 40793, 40806, 40818, 40831, 40844, 40857, 40870, 40883, 40895, 40908, 40921, 40934, 40947, 40960, 40972, 40985, 40998, 41011, 41023,
311  41036, 41049, 41062, 41075, 41087, 41100, 41113, 41126, 41138, 41151, 41164, 41177, 41189, 41202, 41215, 41227, 41240, 41253, 41266, 41278, 41291, 41304,
312  41316, 41329, 41342, 41354, 41367, 41380, 41392, 41405, 41418, 41430, 41443, 41456, 41468, 41481, 41494, 41506, 41519, 41532, 41544, 41557, 41569, 41582,
313  41595, 41607, 41620, 41632, 41645, 41658, 41670, 41683, 41695, 41708, 41720, 41733, 41746, 41758, 41771, 41783, 41796, 41808, 41821, 41833, 41846, 41858,
314  41871, 41883, 41896, 41909, 41921, 41934, 41946, 41959, 41971, 41984, 41996, 42008, 42021, 42033, 42046, 42058, 42071, 42083, 42096, 42108, 42121, 42133,
315  42146, 42158, 42170, 42183, 42195, 42208, 42220, 42233, 42245, 42257, 42270, 42282, 42295, 42307, 42319, 42332, 42344, 42356, 42369, 42381, 42394, 42406,
316  42418, 42431, 42443, 42455, 42468, 42480, 42492, 42505, 42517, 42529, 42542, 42554, 42566, 42579, 42591, 42603, 42616, 42628, 42640, 42653, 42665, 42677,
317  42689, 42702, 42714, 42726, 42738, 42751, 42763, 42775, 42788, 42800, 42812, 42824, 42836, 42849, 42861, 42873, 42885, 42898, 42910, 42922, 42934, 42947,
318  42959, 42971, 42983, 42995, 43008, 43020, 43032, 43044, 43056, 43068, 43081, 43093, 43105, 43117, 43129, 43141, 43154, 43166, 43178, 43190, 43202, 43214,
319  43226, 43238, 43251, 43263, 43275, 43287, 43299, 43311, 43323, 43335, 43347, 43360, 43372, 43384, 43396, 43408, 43420, 43432, 43444, 43456, 43468, 43480,
320  43492, 43504, 43516, 43529, 43541, 43553, 43565, 43577, 43589, 43601, 43613, 43625, 43637, 43649, 43661, 43673, 43685, 43697, 43709, 43721, 43733, 43745,
321  43757, 43769, 43781, 43793, 43805, 43817, 43829, 43841, 43853, 43864, 43876, 43888, 43900, 43912, 43924, 43936, 43948, 43960, 43972, 43984, 43996, 44008,
322  44020, 44032, 44043, 44055, 44067, 44079, 44091, 44103, 44115, 44127, 44139, 44150, 44162, 44174, 44186, 44198, 44210, 44222, 44233, 44245, 44257, 44269,
323  44281, 44293, 44305, 44316, 44328, 44340, 44352, 44364, 44375, 44387, 44399, 44411, 44423, 44434, 44446, 44458, 44470, 44482, 44493, 44505, 44517, 44529,
324  44541, 44552, 44564, 44576, 44588, 44599, 44611, 44623, 44635, 44646, 44658, 44670, 44682, 44693, 44705, 44717, 44728, 44740, 44752, 44764, 44775, 44787,
325  44799, 44810, 44822, 44834, 44846, 44857, 44869, 44881, 44892, 44904, 44916, 44927, 44939, 44951, 44962, 44974, 44986, 44997, 45009, 45021, 45032, 45044,
326  45056, 45067, 45079, 45090, 45102, 45114, 45125, 45137, 45148, 45160, 45172, 45183, 45195, 45207, 45218, 45230, 45241, 45253, 45264, 45276, 45288, 45299,
327  45311, 45322, 45334, 45345, 45357, 45369, 45380, 45392, 45403, 45415, 45426, 45438, 45449, 45461, 45472, 45484, 45496, 45507, 45519, 45530, 45542, 45553,
328  45565, 45576, 45588, 45599, 45611, 45622, 45634, 45645, 45657, 45668, 45680, 45691, 45702, 45714, 45725, 45737, 45748, 45760, 45771, 45783, 45794, 45806,
329  45817, 45829, 45840, 45851, 45863, 45874, 45886, 45897, 45909, 45920, 45931, 45943, 45954, 45966, 45977, 45988, 46000, 46011, 46023, 46034, 46045, 46057,
330  46068, 46080, 46091, 46102, 46114, 46125, 46136, 46148, 46159, 46170, 46182, 46193, 46204, 46216, 46227, 46239, 46250, 46261, 46273, 46284, 46295, 46306,
331  46318, 46329, 46340, 46352, 46363, 46374, 46386, 46397, 46408, 46420, 46431, 46442, 46453, 46465, 46476, 46487, 46499, 46510, 46521, 46532, 46544, 46555,
332  46566, 46577, 46589, 46600, 46611, 46622, 46634, 46645, 46656, 46667, 46679, 46690, 46701, 46712, 46724, 46735, 46746, 46757, 46768, 46780, 46791, 46802,
333  46813, 46824, 46836, 46847, 46858, 46869, 46880, 46892, 46903, 46914, 46925, 46936, 46947, 46959, 46970, 46981, 46992, 47003, 47014, 47026, 47037, 47048,
334  47059, 47070, 47081, 47092, 47104, 47115, 47126, 47137, 47148, 47159, 47170, 47181, 47192, 47204, 47215, 47226, 47237, 47248, 47259, 47270, 47281, 47292,
335  47303, 47315, 47326, 47337, 47348, 47359, 47370, 47381, 47392, 47403, 47414, 47425, 47436, 47447, 47458, 47469, 47480, 47491, 47503, 47514, 47525, 47536,
336  47547, 47558, 47569, 47580, 47591, 47602, 47613, 47624, 47635, 47646, 47657, 47668, 47679, 47690, 47701, 47712, 47723, 47734, 47745, 47756, 47767, 47778,
337  47789, 47800, 47811, 47822, 47832, 47843, 47854, 47865, 47876, 47887, 47898, 47909, 47920, 47931, 47942, 47953, 47964, 47975, 47986, 47997, 48008, 48018,
338  48029, 48040, 48051, 48062, 48073, 48084, 48095, 48106, 48117, 48128, 48138, 48149, 48160, 48171, 48182, 48193, 48204, 48215, 48225, 48236, 48247, 48258,
339  48269, 48280, 48291, 48301, 48312, 48323, 48334, 48345, 48356, 48367, 48377, 48388, 48399, 48410, 48421, 48432, 48442, 48453, 48464, 48475, 48486, 48496,
340  48507, 48518, 48529, 48540, 48550, 48561, 48572, 48583, 48594, 48604, 48615, 48626, 48637, 48648, 48658, 48669, 48680, 48691, 48701, 48712, 48723, 48734,
341  48744, 48755, 48766, 48777, 48787, 48798, 48809, 48820, 48830, 48841, 48852, 48863, 48873, 48884, 48895, 48906, 48916, 48927, 48938, 48948, 48959, 48970,
342  48981, 48991, 49002, 49013, 49023, 49034, 49045, 49055, 49066, 49077, 49087, 49098, 49109, 49119, 49130, 49141, 49152, 49162, 49173, 49183, 49194, 49205,
343  49215, 49226, 49237, 49247, 49258, 49269, 49279, 49290, 49301, 49311, 49322, 49333, 49343, 49354, 49364, 49375, 49386, 49396, 49407, 49417, 49428, 49439,
344  49449, 49460, 49470, 49481, 49492, 49502, 49513, 49523, 49534, 49545, 49555, 49566, 49576, 49587, 49597, 49608, 49619, 49629, 49640, 49650, 49661, 49671,
345  49682, 49693, 49703, 49714, 49724, 49735, 49745, 49756, 49766, 49777, 49787, 49798, 49808, 49819, 49829, 49840, 49851, 49861, 49872, 49882, 49893, 49903,
346  49914, 49924, 49935, 49945, 49956, 49966, 49977, 49987, 49998, 50008, 50019, 50029, 50039, 50050, 50060, 50071, 50081, 50092, 50102, 50113, 50123, 50134,
347  50144, 50155, 50165, 50176, 50186, 50196, 50207, 50217, 50228, 50238, 50249, 50259, 50269, 50280, 50290, 50301, 50311, 50322, 50332, 50342, 50353, 50363,
348  50374, 50384, 50394, 50405, 50415, 50426, 50436, 50446, 50457, 50467, 50478, 50488, 50498, 50509, 50519, 50530, 50540, 50550, 50561, 50571, 50581, 50592,
349  50602, 50612, 50623, 50633, 50644, 50654, 50664, 50675, 50685, 50695, 50706, 50716, 50726, 50737, 50747, 50757, 50768, 50778, 50788, 50799, 50809, 50819,
350  50830, 50840, 50850, 50860, 50871, 50881, 50891, 50902, 50912, 50922, 50933, 50943, 50953, 50963, 50974, 50984, 50994, 51005, 51015, 51025, 51035, 51046,
351  51056, 51066, 51076, 51087, 51097, 51107, 51118, 51128, 51138, 51148, 51159, 51169, 51179, 51189, 51200, 51210, 51220, 51230, 51240, 51251, 51261, 51271,
352  51281, 51292, 51302, 51312, 51322, 51332, 51343, 51353, 51363, 51373, 51383, 51394, 51404, 51414, 51424, 51434, 51445, 51455, 51465, 51475, 51485, 51496,
353  51506, 51516, 51526, 51536, 51546, 51557, 51567, 51577, 51587, 51597, 51607, 51618, 51628, 51638, 51648, 51658, 51668, 51679, 51689, 51699, 51709, 51719,
354  51729, 51739, 51750, 51760, 51770, 51780, 51790, 51800, 51810, 51820, 51830, 51841, 51851, 51861, 51871, 51881, 51891, 51901, 51911, 51921, 51932, 51942,
355  51952, 51962, 51972, 51982, 51992, 52002, 52012, 52022, 52032, 52042, 52053, 52063, 52073, 52083, 52093, 52103, 52113, 52123, 52133, 52143, 52153, 52163,
356  52173, 52183, 52193, 52203, 52213, 52224, 52234, 52244, 52254, 52264, 52274, 52284, 52294, 52304, 52314, 52324, 52334, 52344, 52354, 52364, 52374, 52384,
357  52394, 52404, 52414, 52424, 52434, 52444, 52454, 52464, 52474, 52484, 52494, 52504, 52514, 52524, 52534, 52544, 52554, 52564, 52574, 52584, 52594, 52604,
358  52614, 52624, 52633, 52643, 52653, 52663, 52673, 52683, 52693, 52703, 52713, 52723, 52733, 52743, 52753, 52763, 52773, 52783, 52793, 52803, 52812, 52822,
359  52832, 52842, 52852, 52862, 52872, 52882, 52892, 52902, 52912, 52922, 52931, 52941, 52951, 52961, 52971, 52981, 52991, 53001, 53011, 53021, 53030, 53040,
360  53050, 53060, 53070, 53080, 53090, 53100, 53109, 53119, 53129, 53139, 53149, 53159, 53169, 53179, 53188, 53198, 53208, 53218, 53228, 53238, 53248, 53257,
361  53267, 53277, 53287, 53297, 53307, 53316, 53326, 53336, 53346, 53356, 53366, 53375, 53385, 53395, 53405, 53415, 53424, 53434, 53444, 53454, 53464, 53473,
362  53483, 53493, 53503, 53513, 53522, 53532, 53542, 53552, 53562, 53571, 53581, 53591, 53601, 53611, 53620, 53630, 53640, 53650, 53659, 53669, 53679, 53689,
363  53699, 53708, 53718, 53728, 53738, 53747, 53757, 53767, 53777, 53786, 53796, 53806, 53816, 53825, 53835, 53845, 53855, 53864, 53874, 53884, 53893, 53903,
364  53913, 53923, 53932, 53942, 53952, 53961, 53971, 53981, 53991, 54000, 54010, 54020, 54029, 54039, 54049, 54059, 54068, 54078, 54088, 54097, 54107, 54117,
365  54126, 54136, 54146, 54155, 54165, 54175, 54184, 54194, 54204, 54214, 54223, 54233, 54243, 54252, 54262, 54272, 54281, 54291, 54300, 54310, 54320, 54329,
366  54339, 54349, 54358, 54368, 54378, 54387, 54397, 54407, 54416, 54426, 54435, 54445, 54455, 54464, 54474, 54484, 54493, 54503, 54512, 54522, 54532, 54541,
367  54551, 54561, 54570, 54580, 54589, 54599, 54609, 54618, 54628, 54637, 54647, 54657, 54666, 54676, 54685, 54695, 54704, 54714, 54724, 54733, 54743, 54752,
368  54762, 54772, 54781, 54791, 54800, 54810, 54819, 54829, 54839, 54848, 54858, 54867, 54877, 54886, 54896, 54905, 54915, 54924, 54934, 54944, 54953, 54963,
369  54972, 54982, 54991, 55001, 55010, 55020, 55029, 55039, 55048, 55058, 55067, 55077, 55087, 55096, 55106, 55115, 55125, 55134, 55144, 55153, 55163, 55172,
370  55182, 55191, 55201, 55210, 55220, 55229, 55239, 55248, 55258, 55267, 55277, 55286, 55296, 55305, 55314, 55324, 55333, 55343, 55352, 55362, 55371, 55381,
371  55390, 55400, 55409, 55419, 55428, 55438, 55447, 55456, 55466, 55475, 55485, 55494, 55504, 55513, 55523, 55532, 55541, 55551, 55560, 55570, 55579, 55589,
372  55598, 55608, 55617, 55626, 55636, 55645, 55655, 55664, 55673, 55683, 55692, 55702, 55711, 55721, 55730, 55739, 55749, 55758, 55768, 55777, 55786, 55796,
373  55805, 55815, 55824, 55833, 55843, 55852, 55861, 55871, 55880, 55890, 55899, 55908, 55918, 55927, 55937, 55946, 55955, 55965, 55974, 55983, 55993, 56002,
374  56011, 56021, 56030, 56040, 56049, 56058, 56068, 56077, 56086, 56096, 56105, 56114, 56124, 56133, 56142, 56152, 56161, 56170, 56180, 56189, 56198, 56208,
375  56217, 56226, 56236, 56245, 56254, 56264, 56273, 56282, 56292, 56301, 56310, 56320, 56329, 56338, 56347, 56357, 56366, 56375, 56385, 56394, 56403, 56413,
376  56422, 56431, 56440, 56450, 56459, 56468, 56478, 56487, 56496, 56505, 56515, 56524, 56533, 56542, 56552, 56561, 56570, 56580, 56589, 56598, 56607, 56617,
377  56626, 56635, 56644, 56654, 56663, 56672, 56681, 56691, 56700, 56709, 56718, 56728, 56737, 56746, 56755, 56765, 56774, 56783, 56792, 56802, 56811, 56820,
378  56829, 56838, 56848, 56857, 56866, 56875, 56885, 56894, 56903, 56912, 56921, 56931, 56940, 56949, 56958, 56967, 56977, 56986, 56995, 57004, 57013, 57023,
379  57032, 57041, 57050, 57059, 57069, 57078, 57087, 57096, 57105, 57114, 57124, 57133, 57142, 57151, 57160, 57170, 57179, 57188, 57197, 57206, 57215, 57225,
380  57234, 57243, 57252, 57261, 57270, 57279, 57289, 57298, 57307, 57316, 57325, 57334, 57344, 57353, 57362, 57371, 57380, 57389, 57398, 57407, 57417, 57426,
381  57435, 57444, 57453, 57462, 57471, 57480, 57490, 57499, 57508, 57517, 57526, 57535, 57544, 57553, 57563, 57572, 57581, 57590, 57599, 57608, 57617, 57626,
382  57635, 57644, 57654, 57663, 57672, 57681, 57690, 57699, 57708, 57717, 57726, 57735, 57744, 57753, 57763, 57772, 57781, 57790, 57799, 57808, 57817, 57826,
383  57835, 57844, 57853, 57862, 57871, 57880, 57889, 57899, 57908, 57917, 57926, 57935, 57944, 57953, 57962, 57971, 57980, 57989, 57998, 58007, 58016, 58025,
384  58034, 58043, 58052, 58061, 58070, 58079, 58088, 58097, 58106, 58115, 58124, 58133, 58143, 58152, 58161, 58170, 58179, 58188, 58197, 58206, 58215, 58224,
385  58233, 58242, 58251, 58260, 58269, 58278, 58287, 58296, 58305, 58314, 58323, 58332, 58341, 58350, 58359, 58368, 58376, 58385, 58394, 58403, 58412, 58421,
386  58430, 58439, 58448, 58457, 58466, 58475, 58484, 58493, 58502, 58511, 58520, 58529, 58538, 58547, 58556, 58565, 58574, 58583, 58592, 58601, 58610, 58618,
387  58627, 58636, 58645, 58654, 58663, 58672, 58681, 58690, 58699, 58708, 58717, 58726, 58735, 58744, 58752, 58761, 58770, 58779, 58788, 58797, 58806, 58815,
388  58824, 58833, 58842, 58851, 58859, 58868, 58877, 58886, 58895, 58904, 58913, 58922, 58931, 58940, 58948, 58957, 58966, 58975, 58984, 58993, 59002, 59011,
389  59020, 59028, 59037, 59046, 59055, 59064, 59073, 59082, 59091, 59099, 59108, 59117, 59126, 59135, 59144, 59153, 59162, 59170, 59179, 59188, 59197, 59206,
390  59215, 59224, 59232, 59241, 59250, 59259, 59268, 59277, 59285, 59294, 59303, 59312, 59321, 59330, 59339, 59347, 59356, 59365, 59374, 59383, 59392, 59400,
391  59409, 59418, 59427, 59436, 59444, 59453, 59462, 59471, 59480, 59489, 59497, 59506, 59515, 59524, 59533, 59541, 59550, 59559, 59568, 59577, 59585, 59594,
392  59603, 59612, 59621, 59629, 59638, 59647, 59656, 59665, 59673, 59682, 59691, 59700, 59708, 59717, 59726, 59735, 59744, 59752, 59761, 59770, 59779, 59787,
393  59796, 59805, 59814, 59822, 59831, 59840, 59849, 59858, 59866, 59875, 59884, 59893, 59901, 59910, 59919, 59928, 59936, 59945, 59954, 59963, 59971, 59980,
394  59989, 59998, 60006, 60015, 60024, 60032, 60041, 60050, 60059, 60067, 60076, 60085, 60094, 60102, 60111, 60120, 60128, 60137, 60146, 60155, 60163, 60172,
395  60181, 60189, 60198, 60207, 60216, 60224, 60233, 60242, 60250, 60259, 60268, 60276, 60285, 60294, 60303, 60311, 60320, 60329, 60337, 60346, 60355, 60363,
396  60372, 60381, 60389, 60398, 60407, 60416, 60424, 60433, 60442, 60450, 60459, 60468, 60476, 60485, 60494, 60502, 60511, 60520, 60528, 60537, 60546, 60554,
397  60563, 60572, 60580, 60589, 60597, 60606, 60615, 60623, 60632, 60641, 60649, 60658, 60667, 60675, 60684, 60693, 60701, 60710, 60718, 60727, 60736, 60744,
398  60753, 60762, 60770, 60779, 60788, 60796, 60805, 60813, 60822, 60831, 60839, 60848, 60856, 60865, 60874, 60882, 60891, 60900, 60908, 60917, 60925, 60934,
399  60943, 60951, 60960, 60968, 60977, 60986, 60994, 61003, 61011, 61020, 61029, 61037, 61046, 61054, 61063, 61071, 61080, 61089, 61097, 61106, 61114, 61123,
400  61132, 61140, 61149, 61157, 61166, 61174, 61183, 61192, 61200, 61209, 61217, 61226, 61234, 61243, 61251, 61260, 61269, 61277, 61286, 61294, 61303, 61311,
401  61320, 61328, 61337, 61346, 61354, 61363, 61371, 61380, 61388, 61397, 61405, 61414, 61422, 61431, 61440, 61448, 61457, 61465, 61474, 61482, 61491, 61499,
402  61508, 61516, 61525, 61533, 61542, 61550, 61559, 61567, 61576, 61584, 61593, 61601, 61610, 61618, 61627, 61635, 61644, 61652, 61661, 61669, 61678, 61686,
403  61695, 61703, 61712, 61720, 61729, 61737, 61746, 61754, 61763, 61771, 61780, 61788, 61797, 61805, 61814, 61822, 61831, 61839, 61848, 61856, 61865, 61873,
404  61882, 61890, 61899, 61907, 61916, 61924, 61932, 61941, 61949, 61958, 61966, 61975, 61983, 61992, 62000, 62009, 62017, 62026, 62034, 62042, 62051, 62059,
405  62068, 62076, 62085, 62093, 62102, 62110, 62118, 62127, 62135, 62144, 62152, 62161, 62169, 62177, 62186, 62194, 62203, 62211, 62220, 62228, 62236, 62245,
406  62253, 62262, 62270, 62279, 62287, 62295, 62304, 62312, 62321, 62329, 62337, 62346, 62354, 62363, 62371, 62380, 62388, 62396, 62405, 62413, 62422, 62430,
407  62438, 62447, 62455, 62464, 62472, 62480, 62489, 62497, 62505, 62514, 62522, 62531, 62539, 62547, 62556, 62564, 62573, 62581, 62589, 62598, 62606, 62614,
408  62623, 62631, 62640, 62648, 62656, 62665, 62673, 62681, 62690, 62698, 62706, 62715, 62723, 62732, 62740, 62748, 62757, 62765, 62773, 62782, 62790, 62798,
409  62807, 62815, 62823, 62832, 62840, 62848, 62857, 62865, 62873, 62882, 62890, 62898, 62907, 62915, 62923, 62932, 62940, 62948, 62957, 62965, 62973, 62982,
410  62990, 62998, 63007, 63015, 63023, 63032, 63040, 63048, 63057, 63065, 63073, 63082, 63090, 63098, 63106, 63115, 63123, 63131, 63140, 63148, 63156, 63165,
411  63173, 63181, 63190, 63198, 63206, 63214, 63223, 63231, 63239, 63248, 63256, 63264, 63272, 63281, 63289, 63297, 63306, 63314, 63322, 63330, 63339, 63347,
412  63355, 63364, 63372, 63380, 63388, 63397, 63405, 63413, 63421, 63430, 63438, 63446, 63454, 63463, 63471, 63479, 63488, 63496, 63504, 63512, 63521, 63529,
413  63537, 63545, 63554, 63562, 63570, 63578, 63587, 63595, 63603, 63611, 63619, 63628, 63636, 63644, 63652, 63661, 63669, 63677, 63685, 63694, 63702, 63710,
414  63718, 63727, 63735, 63743, 63751, 63759, 63768, 63776, 63784, 63792, 63801, 63809, 63817, 63825, 63833, 63842, 63850, 63858, 63866, 63874, 63883, 63891,
415  63899, 63907, 63915, 63924, 63932, 63940, 63948, 63956, 63965, 63973, 63981, 63989, 63997, 64006, 64014, 64022, 64030, 64038, 64047, 64055, 64063, 64071,
416  64079, 64088, 64096, 64104, 64112, 64120, 64128, 64137, 64145, 64153, 64161, 64169, 64177, 64186, 64194, 64202, 64210, 64218, 64226, 64235, 64243, 64251,
417  64259, 64267, 64275, 64284, 64292, 64300, 64308, 64316, 64324, 64332, 64341, 64349, 64357, 64365, 64373, 64381, 64389, 64398, 64406, 64414, 64422, 64430,
418  64438, 64446, 64455, 64463, 64471, 64479, 64487, 64495, 64503, 64512, 64520, 64528, 64536, 64544, 64552, 64560, 64568, 64576, 64585, 64593, 64601, 64609,
419  64617, 64625, 64633, 64641, 64650, 64658, 64666, 64674, 64682, 64690, 64698, 64706, 64714, 64722, 64731, 64739, 64747, 64755, 64763, 64771, 64779, 64787,
420  64795, 64803, 64812, 64820, 64828, 64836, 64844, 64852, 64860, 64868, 64876, 64884, 64892, 64900, 64909, 64917, 64925, 64933, 64941, 64949, 64957, 64965,
421  64973, 64981, 64989, 64997, 65005, 65013, 65021, 65030, 65038, 65046, 65054, 65062, 65070, 65078, 65086, 65094, 65102, 65110, 65118, 65126, 65134, 65142,
422  65150, 65158, 65166, 65175, 65183, 65191, 65199, 65207, 65215, 65223, 65231, 65239, 65247, 65255, 65263, 65271, 65279, 65287, 65295, 65303, 65311, 65319,
423  65327, 65335, 65343, 65351, 65359, 65367, 65375, 65383, 65391, 65399, 65407, 65415, 65423, 65431, 65439, 65447, 65455, 65463, 65471, 65479, 65487, 65495,
424  65503, 65511, 65519, 65527 };
425 
430 #endif // _YI_MATH_TABLES_H_
431 
YI_ATAN_SIZE
const int32_t YI_ATAN_SIZE
Definition: YiMathTables.h:21
YI_ANGLE2PI
const int32_t YI_ANGLE2PI
Definition: YiMathTables.h:15
YI_ANGLEPI
const int32_t YI_ANGLEPI
Definition: YiMathTables.h:16
g_sYICosine
const int16_t g_sYICosine[YI_ANGLE2PI]
Definition: YiMathTables.h:118
YI_PI
const float YI_PI
Definition: YiMathTables.h:18
g_usYISqrt
const uint16_t g_usYISqrt[4096]
Definition: YiMathTables.h:238
YI_TRIG_SHIFT
const int32_t YI_TRIG_SHIFT
Definition: YiMathTables.h:19
YI_ANGLEMASK
const int32_t YI_ANGLEMASK
Definition: YiMathTables.h:17
g_usYIArctan
const uint16_t g_usYIArctan[YI_ATAN_SIZE+1]
Definition: YiMathTables.h:213
YI_TRIG_MUL
const int32_t YI_TRIG_MUL
Definition: YiMathTables.h:20
YI_ANGLESHIFT
const int32_t YI_ANGLESHIFT
Definition: YiMathTables.h:14
g_sYISine
const int16_t g_sYISine[YI_ANGLE2PI]
Definition: YiMathTables.h:23