| /branches/V0.76g-acid/mymath.c |
|---|
| 0,0 → 1,106 |
| #include <stdlib.h> |
| #include <avr/pgmspace.h> |
| #include "mymath.h" |
| // discrete mathematics |
| // Sinus with argument in degree at an angular resolution of 1 degree and a discretisation of 13 bit. |
| 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}; |
| int16_t c_sin_8192(int16_t angle) |
| { |
| int8_t m,n; |
| int16_t sinus; |
| // avoid negative angles |
| if (angle < 0) |
| { |
| m = -1; |
| angle = abs(angle); |
| } |
| else m = +1; |
| // fold angle to intervall 0 to 359 |
| angle %= 360; |
| // check quadrant |
| if (angle <= 90) n=1; // first quadrant |
| else if ((angle > 90) && (angle <= 180)) {angle = 180 - angle; n = 1;} // second quadrant |
| else if ((angle > 180) && (angle <= 270)) {angle = angle - 180; n = -1;} // third quadrant |
| else {angle = 360 - angle; n = -1;} //fourth quadrant |
| // get lookup value |
| sinus = pgm_read_word(&pgm_sinlookup[angle]); |
| // calculate sinus value |
| return (sinus * m * n); |
| } |
| // Cosinus with argument in degree at an angular resolution of 1 degree and a discretisation of 13 bit. |
| int16_t c_cos_8192(int16_t angle) |
| { |
| return (c_sin_8192(90 - angle)); |
| } |
| // Arcustangens returns degree in a range of +/. 180 deg |
| 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}; |
| int16_t c_atan2(int16_t y, int16_t x) |
| { |
| int16_t index, angle; |
| int8_t m; |
| if (!x && !y) return 0; //atan2(0, 0) is undefined |
| if (y < 0) m = -1; |
| else m = 1; |
| if (!x) return (90 * m); // atan2(y,0) = +/- 90 deg |
| index = (int16_t)(((int32_t)y * 64) / x);// calculate index for lookup table |
| if (index < 0) index = -index; |
| if (index < 346) angle = pgm_read_byte(&pgm_atanlookup[index]); // lookup for 0 deg to 79 deg |
| else if (index > 7334) angle = 90; // limit is 90 deg |
| else if (index > 2444) angle = 89; // 89 deg to 80 deg is mapped via intervalls |
| else if (index > 1465) angle = 88; |
| else if (index > 1046) angle = 87; |
| else if (index > 813) angle = 86; |
| else if (index > 664) angle = 85; |
| else if (index > 561) angle = 84; |
| else if (index > 486) angle = 83; |
| else if (index > 428) angle = 82; |
| else if (index > 382) angle = 81; |
| else angle = 80; // (index>345) |
| if (x > 0) return (angle * m); // 1st and 4th quadrant |
| else if ((x < 0) && (m > 0)) return (180 - angle); // 2nd quadrant |
| else return (angle - 180); // ( (x < 0) && (y < 0)) 3rd quadrant |
| } |
| // Integer square root |
| // For details of the algorithm see the article http://www.embedded.com/98/9802fe2.htm |
| uint32_t c_sqrt(uint32_t a) |
| { |
| uint32_t rem = 0; |
| uint32_t root = 0; |
| uint8_t i; |
| for(i = 0; i < 16; i++) |
| { |
| root <<= 1; |
| rem = ((rem << 2) + (a >> 30)); |
| a <<= 2; |
| root++; |
| if(root <= rem) |
| { |
| rem -= root; |
| root++; |
| } |
| else root--; |
| } |
| return (root >> 1); |
| } |