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| 205 | Nick666 | 1 | /* |
| 2 | This program (files math.c and math.h) is free software; you can redistribute it and/or modify |
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| 3 | it under the terms of the GNU General Public License as published by the Free Software Foundation; |
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| 4 | either version 3 of the License, or (at your option) any later version. |
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| 5 | This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; |
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| 6 | without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 7 | GNU General Public License for more details. You should have received a copy of the GNU General Public License |
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| 8 | along with this program. If not, see <http://www.gnu.org/licenses/>. |
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| 9 | |||
| 10 | Please note: All the other files for the project "Mikrokopter" by H.Buss are under the license (license_buss.txt) published by www.mikrokopter.de |
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| 11 | */ |
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| 12 | |||
| 13 | #include "main.h" |
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| 14 | |||
| 232 | Nick666 | 15 | /* |
| 205 | Nick666 | 16 | //----------------------------------------------- |
| 226 | Nick666 | 17 | // Fast arctan2 with max error of .07 rads |
| 205 | Nick666 | 18 | // http://www.dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm |
| 19 | //----------------------------------------------- |
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| 229 | Nick666 | 20 | signed int arctan_f(signed int x, signed int y) |
| 205 | Nick666 | 21 | { |
| 226 | Nick666 | 22 | float rad,r; |
| 23 | short int m; |
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| 24 | #define coeff_1 0.7854 |
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| 25 | #define coeff_2 2.3562 |
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| 26 | #define rad2grad 57.2958 |
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| 205 | Nick666 | 27 | |
| 28 | if (!x && !y) return 0; |
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| 29 | |||
| 30 | if (y < 0) {y = abs(y); m = -1;} |
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| 31 | else m = 1; |
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| 32 | |||
| 33 | if (x>=0) |
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| 34 | { |
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| 226 | Nick666 | 35 | r = (float)(x - y) / (float)(x + y); |
| 36 | rad = coeff_1 - coeff_1*r; |
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| 205 | Nick666 | 37 | } |
| 38 | else |
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| 39 | { |
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| 226 | Nick666 | 40 | r = (float)(x + y) / (float)(y - x); |
| 41 | rad = coeff_2 - coeff_1*r; |
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| 205 | Nick666 | 42 | } |
| 226 | Nick666 | 43 | |
| 44 | rad *= rad2grad; |
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| 45 | |||
| 214 | Nick666 | 46 | return(rad*m); |
| 205 | Nick666 | 47 | } |
| 232 | Nick666 | 48 | */ |
| 205 | Nick666 | 49 | |
| 232 | Nick666 | 50 | const uint8_t pgm_atan[270] PROGMEM = {0,1,2,3,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,27,28,29,30,31,32,33,33,34,35,36,37,37,38,39,39,40,41,41,42,43,43,44,44,45,46,46,47,47,48,48,49,49,50,50,51,51,52,52,52,53,53,54,54,54,55,55,56,56,56,57,57,57,58,58,58,59,59,59,60,60,60,60,61,61,61,61,62,62,62,62,63,63,63,63,64,64,64,64,65,65,65,65,65,66,66,66,66,66,67,67,67,67,67,67,68,68,68,68,68,68,69,69,69,69,69,69,69,70,70,70,70,70,70,70,70,71,71,71,71,71,71,71,71,72,72,72,72,72,72,72,72,72,73,73,73,73,73,73,73,73,73,73,74,74,74,74,74,74,74,74,74,74,74,74,75,75,75,75,75,75,75,75,75,75,75,75,75,76,76,76,76,76,76,76,76,76,76,76,76,76,76,76,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79}; |
| 51 | |||
| 226 | Nick666 | 52 | signed int arctan_i(signed int x, signed int y) |
| 214 | Nick666 | 53 | { |
| 232 | Nick666 | 54 | int i,angle; |
| 55 | int8_t m; |
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| 214 | Nick666 | 56 | |
| 232 | Nick666 | 57 | if (!x && !y) return 0; //atan2 = 0 für x und y = 0 |
| 58 | |||
| 59 | if (y < 0) m=-1; |
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| 60 | else m=1; |
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| 61 | |||
| 62 | if (x==0) return (90*m); // atan2 = 90° für x = 0 |
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| 63 | |||
| 64 | i = abs(((float)y / x) * 50.0); // Berechne i für die Lookup table (Schrittweite atan(x) ist 0.02 -> *50) |
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| 214 | Nick666 | 65 | |
| 232 | Nick666 | 66 | if (i<270) angle = pgm_read_byte(&pgm_atan[i]); // Lookup für 1° bis 79° |
| 67 | else if (i>5750) angle = 90; // Grenzwert ist 90° |
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| 68 | else if (i>=1910) angle = 89; // 89° bis 80° über Wertebereiche |
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| 69 | else if (i>=1150) angle = 88; |
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| 70 | else if (i>=820) angle = 87; |
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| 71 | else if (i>=640) angle = 86; |
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| 72 | else if (i>=520) angle = 85; |
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| 73 | else if (i>=440) angle = 84; |
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| 74 | else if (i>=380) angle = 83; |
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| 75 | else if (i>=335) angle = 82; |
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| 76 | else if (i>=299) angle = 81; |
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| 77 | else angle = 80; // (i>=270) |
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| 226 | Nick666 | 78 | |
| 232 | Nick666 | 79 | if (x > 0) return (angle*m); // Quadrant I und IV |
| 80 | else if ((x < 0) && (y >= 0)) return ((angle*-1) + 180); // Quadrant II |
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| 81 | else return (angle - 180); // x < 0 && y < 0 Quadrant III |
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| 214 | Nick666 | 82 | } |
| 83 | |||
| 226 | Nick666 | 84 | |
| 85 | |||
| 86 | |||
| 229 | Nick666 | 87 | |
| 88 | const float pgm_sinus_f [91] PROGMEM = {0.000,0.017,0.035,0.052,0.070,0.087,0.105,0.122,0.139,0.156,0.174,0.191,0.208,0.225,0.242,0.259,0.276,0.292,0.309,0.326,0.342,0.358,0.375,0.391,0.407,0.423,0.438,0.454,0.469,0.485,0.500,0.515,0.530,0.545,0.559,0.574,0.588,0.602,0.616,0.629,0.643,0.656,0.669,0.682,0.695,0.707,0.719,0.731,0.743,0.755,0.766,0.777,0.788,0.799,0.809,0.819,0.829,0.839,0.848,0.857,0.866,0.875,0.883,0.891,0.899,0.906,0.914,0.921,0.927,0.934,0.940,0.946,0.951,0.956,0.961,0.966,0.970,0.974,0.978,0.982,0.985,0.988,0.990,0.993,0.995,0.996,0.998,0.999,0.999,1.000,1.000}; |
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| 89 | |||
| 90 | inline float pgm_read_float(const float *addr) |
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| 91 | { |
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| 92 | union |
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| 93 | { |
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| 94 | uint16_t i[2]; // 2 16-bit-Worte |
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| 95 | float f; |
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| 96 | } u; |
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| 97 | |||
| 98 | u.i[0]=pgm_read_word((PGM_P)addr); |
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| 99 | u.i[1]=pgm_read_word((PGM_P)addr+2); |
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| 100 | |||
| 101 | return u.f; |
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| 102 | } |
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| 103 | |||
| 104 | // cosinus Funktion: Eingabewert Winkel in Grad |
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| 105 | float cos_f(signed int winkel) |
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| 106 | { |
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| 107 | return (sin_f(90-winkel)); |
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| 205 | Nick666 | 108 | } |
| 109 | |||
| 229 | Nick666 | 110 | // sinus Funktion: Eingabewert Winkel in Grad |
| 111 | float sin_f(signed int winkel) |
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| 205 | Nick666 | 112 | { |
| 113 | short int m,n; |
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| 229 | Nick666 | 114 | float sinus; |
| 205 | Nick666 | 115 | |
| 116 | //winkel = winkel % 360; |
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| 117 | |||
| 118 | if (winkel < 0) |
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| 119 | { |
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| 120 | m = -1; |
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| 121 | winkel = abs(winkel); |
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| 122 | } |
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| 123 | else m = +1; |
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| 124 | |||
| 125 | // Quadranten auswerten |
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| 126 | if ((winkel > 90 ) && (winkel <= 180)) {winkel = 180 - winkel; n = 1;} |
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| 127 | else if ((winkel > 180 ) && (winkel <= 270)) {winkel = winkel - 180; n = -1;} |
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| 128 | else if ((winkel > 270) && (winkel <= 360)) {winkel = 360 - winkel; n = -1;} |
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| 129 | else n = 1; //0 - 90 Grad |
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| 130 | |||
| 229 | Nick666 | 131 | sinus = pgm_read_float(&pgm_sinus_f[winkel]); |
| 205 | Nick666 | 132 | |
| 229 | Nick666 | 133 | return (sinus*m*n); |
| 205 | Nick666 | 134 | } |
| 135 | |||
| 136 | |||
| 232 | Nick666 | 137 | /* |
| 226 | Nick666 | 138 | |
| 229 | Nick666 | 139 | const unsigned int pgm_sinus[91] PROGMEM = {0,17,35,52,70,87,105,122,139,156,174,191,208,225,242,259,276,292,309,326,342,358,375,391,407,423,438,454,469,485,500,515,530,545,559,574,588,602,616,629,643,656,669,682,695,707,719,731,743,755,766,777,788,799,809,819,829,839,848,857,866,875,883,891,899,906,914,921,927,934,940,946,951,956,961,966,970,974,978,982,985,988,990,993,995,996,998,999,999,1000,1000}; |
| 140 | |||
| 141 | // cosinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =cos(winkel)*1000 |
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| 142 | signed int cos_i(signed int winkel) |
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| 143 | { |
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| 144 | return (sin_i(90-winkel)); |
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| 226 | Nick666 | 145 | } |
| 146 | |||
| 229 | Nick666 | 147 | // sinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =sin(winkel)*1000 |
| 148 | signed int sin_i(signed int winkel) |
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| 226 | Nick666 | 149 | { |
| 150 | short int m,n; |
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| 151 | |||
| 152 | //winkel = winkel % 360; |
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| 153 | |||
| 154 | if (winkel < 0) |
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| 155 | { |
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| 156 | m = -1; |
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| 157 | winkel = abs(winkel); |
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| 158 | } |
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| 159 | else m = +1; |
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| 160 | |||
| 161 | // Quadranten auswerten |
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| 162 | if ((winkel > 90 ) && (winkel <= 180)) {winkel = 180 - winkel; n = 1;} |
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| 163 | else if ((winkel > 180 ) && (winkel <= 270)) {winkel = winkel - 180; n = -1;} |
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| 164 | else if ((winkel > 270) && (winkel <= 360)) {winkel = 360 - winkel; n = -1;} |
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| 165 | else n = 1; //0 - 90 Grad |
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| 166 | |||
| 229 | Nick666 | 167 | winkel = pgm_read_word(&pgm_sinus[winkel]); |
| 226 | Nick666 | 168 | |
| 229 | Nick666 | 169 | return (winkel*m*n); |
| 226 | Nick666 | 170 | } |
| 232 | Nick666 | 171 | */ |