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838 MikeW 1 
#include <stdlib.h>
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#include <avr/pgmspace.h>
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#include "mymath.h"
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#include "main.h"
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// discrete mathematics
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7 
// Sinus with argument in degree at an angular resolution of 1 degree and a discretisation of 13 bit.
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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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int16_t c_sin_8192(int16_t angle)
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{
966 MikeW 12 
  int8_t m,n;
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  int16_t sinus;
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  // avoid negative angles
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  if (angle < 0)
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  {
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    m = -1;
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    angle = abs(angle);
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  }
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  else m = +1;
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  // fold angle to intervall 0 to 359
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  angle %= 360;
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  // check quadrant
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  if (angle <= 90) n=1; // first quadrant
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  else if ((angle > 90) && (angle <= 180)) {angle = 180 - angle; n = 1;} // second quadrant
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  else if ((angle > 180) && (angle <= 270)) {angle = angle - 180; n = -1;} // third quadrant
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  else {angle = 360 - angle; n = -1;}   //fourth quadrant
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  // get lookup value
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  sinus = pgm_read_word(&pgm_sinlookup[angle]);
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  // calculate sinus value
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  return (sinus * m * n);
838 MikeW 35 
}
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// Cosinus with argument in degree at an angular resolution of 1 degree and a discretisation of 13 bit.
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int16_t c_cos_8192(int16_t angle)
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{
966 MikeW 40 
  return (c_sin_8192(90 - angle));
838 MikeW 41 
}
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// Arcustangens returns degree in a range of +/. 180 deg
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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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int16_t c_atan2(int16_t y, int16_t x)
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{
966 MikeW 48 
  int16_t index, angle;
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  int8_t m;
50 
 
51 
  if (!x && !y) return 0;               //atan2(0, 0) is undefined
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53 
  if (y < 0) m = -1;
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  else m = 1;
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56 
  if (!x) return (90 * m);              // atan2(y,0) = +/- 90 deg
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58 
  index = (int16_t)(((int32_t)y * 64) / x);// calculate index for lookup table
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  if (index < 0) index = -index;
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61 
  if (index < 346) angle = pgm_read_byte(&pgm_atanlookup[index]);       // lookup for 0 deg to 79 deg
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  else if (index > 7334) angle = 90;                                            // limit is 90 deg
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  else if (index > 2444) angle = 89;                                            // 89 deg to 80 deg is mapped via intervalls
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  else if (index > 1465) angle = 88;
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  else if (index > 1046) angle = 87;
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  else if (index > 813) angle = 86;
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  else if (index > 664) angle = 85;
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  else if (index > 561) angle = 84;
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  else if (index > 486) angle = 83;
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  else if (index > 428) angle = 82;
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  else if (index > 382) angle = 81;
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  else angle = 80; // (index>345)
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74 
  if (x > 0) return (angle * m);        // 1st and 4th quadrant
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  else if ((x < 0) && (m > 0)) return (180 - angle);    // 2nd quadrant
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  else return (angle - 180); // ( (x < 0) && (y < 0))   3rd quadrant
838 MikeW 77 
}
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79 
// Arcustangens returns degree in a range of +/. 180 deg
80 
const uint8_t pgm_asinlookup[128] PROGMEM = {0,0,1,1,2,2,3,3,4,4,4,5,5,6,6,7,7,8,8,9,9,9,10,10,11,11,12,12,13,13,14,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,31,31,32,32,33,33,34,34,35,35,36,36,37,38,38,39,39,40,40,41,42,42,43,43,44,45,45,46,47,47,48,49,49,50,51,51,52,53,54,54,55,56,57,58,58,59,60,61,62,63,64,65,66,67,68,70,71,72,74,76,78,80,83};
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82 
int c_asin_8192(int y)
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{
966 MikeW 84 
  int index, m;
85 
  if (y < 0)
86 
  {    
87 
    m = -1;
88 
    index = -y / 64;
89 
  }
90 
  else
91 
  {
92 
    m = 1;
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    index = y / 64;
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  }    
95 
 
96 
  if (index > 127)
97 
  {    
98 
    index = 127;
99 
  }
100 
  return(m * pgm_read_byte(&pgm_asinlookup[index]));
838 MikeW 101 
}
102 
// integer square root
103 
uint32_t c_sqrt(uint32_t number)
104 
{
966 MikeW 105 
  uint32_t s1, s2;
106 
  uint8_t iter = 0;
107 
  // initialization of iteration
108 
  s2 = number;
109 
  do // iterative formula to solve x^2 - n = 0
110 
  {
111 
    s1 = s2;
112 
    s2 = number / s1;
113 
    s2 += s1;
114 
    s2 /= 2;
115 
    iter++;
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    //if(iter > 40) break;
117 
  }while( ( (s1-s2) > 1) && (iter < 40));
118 
  return s2;
838 MikeW 119 
}