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| Rev | Author | Line No. | Line |
|---|---|---|---|
| 1388 | Arthur | 1 | #include <stdlib.h> |
| 2 | #include <avr/pgmspace.h> |
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| 3 | #include "mymath.h" |
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| 4 | |||
| 5 | // discrete mathematics |
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| 6 | |||
| 7 | // Sinus with argument in degree at an angular resolution of 1 degree and a discretisation of 13 bit. |
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| 8 | const uint16_t pgm_sinlookup[91] PROGMEM = {0, 143, 286, 429, 571, 714, 856, 998, 1140, 1282, 1423, 1563, 1703, 1843, 1982, 2120, 2258, 2395, 2531, 2667, 2802, 2936, 3069, 3201, 3332, 3462, 3591, 3719, 3846, 3972, 4096, 4219, 4341, 4462, 4581, 4699, 4815, 4930, 5043, 5155, 5266, 5374, 5482, 5587, 5691, 5793, 5893, 5991, 6088, 6183, 6275, 6366, 6455, 6542, 6627, 6710, 6791, 6870, 6947, 7022, 7094, 7165, 7233, 7299, 7363, 7424, 7484, 7541, 7595, 7648, 7698, 7746, 7791, 7834, 7875, 7913, 7949, 7982, 8013, 8041, 8068, 8091, 8112, 8131, 8147, 8161, 8172, 8181, 8187, 8191, 8192}; |
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| 9 | |||
| 10 | int16_t c_sin_8192(int16_t angle) |
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| 11 | { |
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| 12 | int8_t m,n; |
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| 13 | int16_t sinus; |
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| 14 | |||
| 15 | // avoid negative angles |
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| 16 | if (angle < 0) |
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| 17 | { |
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| 18 | m = -1; |
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| 19 | angle = abs(angle); |
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| 20 | } |
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| 21 | else m = +1; |
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| 22 | |||
| 23 | // fold angle to intervall 0 to 359 |
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| 24 | angle %= 360; |
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| 25 | |||
| 26 | // check quadrant |
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| 27 | if (angle <= 90) n=1; // first quadrant |
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| 28 | else if ((angle > 90) && (angle <= 180)) {angle = 180 - angle; n = 1;} // second quadrant |
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| 29 | else if ((angle > 180) && (angle <= 270)) {angle = angle - 180; n = -1;} // third quadrant |
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| 30 | else {angle = 360 - angle; n = -1;} //fourth quadrant |
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| 31 | // get lookup value |
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| 32 | sinus = pgm_read_word(&pgm_sinlookup[angle]); |
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| 33 | // calculate sinus value |
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| 34 | return (sinus * m * n); |
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| 35 | } |
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| 36 | |||
| 37 | // Cosinus with argument in degree at an angular resolution of 1 degree and a discretisation of 13 bit. |
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| 38 | int16_t c_cos_8192(int16_t angle) |
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| 39 | { |
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| 40 | return (c_sin_8192(90 - angle)); |
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| 41 | } |
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| 42 | |||
| 43 | |||
| 44 | // Arcustangens returns degree in a range of +/. 180 deg |
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| 45 | const uint8_t pgm_atanlookup[346] PROGMEM = {0,1,2,3,4,4,5,6,7,8,9,10,11,11,12,13,14,15,16,17,17,18,19,20,21,21,22,23,24,24,25,26,27,27,28,29,29,30,31,31,32,33,33,34,35,35,36,36,37,37,38,39,39,40,40,41,41,42,42,43,43,44,44,45,45,45,46,46,47,47,48,48,48,49,49,50,50,50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,55,56,56,56,57,57,57,57,58,58,58,58,59,59,59,59,60,60,60,60,60,61,61,61,61,62,62,62,62,62,63,63,63,63,63,63,64,64,64,64,64,64,65,65,65,65,65,65,66,66,66,66,66,66,66,67,67,67,67,67,67,67,68,68,68,68,68,68,68,68,69,69,69,69,69,69,69,69,69,70,70,70,70,70,70,70,70,70,71,71,71,71,71,71,71,71,71,71,71,72,72,72,72,72,72,72,72,72,72,72,73,73,73,73,73,73,73,73,73,73,73,73,73,73,74,74,74,74,74,74,74,74,74,74,74,74,74,74,75,75,75,75,75,75,75,75,75,75,75,75,75,75,75,75,75,76,76,76,76,76,76,76,76,76,76,76,76,76,76,76,76,76,76,76,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79}; |
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| 46 | |||
| 47 | int16_t c_atan2(int16_t y, int16_t x) |
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| 48 | { |
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| 49 | int16_t index, angle; |
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| 50 | int8_t m; |
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| 51 | |||
| 52 | if (!x && !y) return 0; //atan2(0, 0) is undefined |
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| 53 | |||
| 54 | if (y < 0) m = -1; |
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| 55 | else m = 1; |
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| 56 | |||
| 57 | if (!x) return (90 * m); // atan2(y,0) = +/- 90 deg |
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| 58 | |||
| 59 | index = (int16_t)(((int32_t)y * 64) / x);// calculate index for lookup table |
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| 60 | if (index < 0) index = -index; |
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| 61 | |||
| 62 | if (index < 346) angle = pgm_read_byte(&pgm_atanlookup[index]); // lookup for 0 deg to 79 deg |
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| 63 | else if (index > 7334) angle = 90; // limit is 90 deg |
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| 64 | else if (index > 2444) angle = 89; // 89 deg to 80 deg is mapped via intervalls |
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| 65 | else if (index > 1465) angle = 88; |
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| 66 | else if (index > 1046) angle = 87; |
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| 67 | else if (index > 813) angle = 86; |
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| 68 | else if (index > 664) angle = 85; |
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| 69 | else if (index > 561) angle = 84; |
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| 70 | else if (index > 486) angle = 83; |
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| 71 | else if (index > 428) angle = 82; |
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| 72 | else if (index > 382) angle = 81; |
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| 73 | else angle = 80; // (index>345) |
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| 74 | |||
| 75 | if (x > 0) return (angle * m); // 1st and 4th quadrant |
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| 76 | else if ((x < 0) && (m > 0)) return (180 - angle); // 2nd quadrant |
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| 77 | else return (angle - 180); // ( (x < 0) && (y < 0)) 3rd quadrant |
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| 78 | } |
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| 79 | |||
| 80 | |||
| 81 | // Integer square root |
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| 82 | // For details of the algorithm see the article http://www.embedded.com/98/9802fe2.htm |
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| 83 | uint32_t c_sqrt(uint32_t a) |
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| 84 | { |
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| 85 | uint32_t rem = 0; |
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| 86 | uint32_t root = 0; |
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| 87 | uint8_t i; |
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| 88 | |||
| 89 | for(i = 0; i < 16; i++) |
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| 90 | { |
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| 91 | root <<= 1; |
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| 92 | rem = ((rem << 2) + (a >> 30)); |
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| 93 | a <<= 2; |
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| 94 | root++; |
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| 95 | if(root <= rem) |
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| 96 | { |
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| 97 | rem -= root; |
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| 98 | root++; |
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| 99 | } |
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| 100 | else root--; |
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| 101 | } |
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| 102 | return (root >> 1); |
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| 103 | } |
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| 104 | |||
| 105 | |||
| 106 |