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205 Nick666 1 
/*
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This program (files math.c and math.h) is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by the Free Software Foundation;
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either version 3 of the License, or (at your option) any later version.  
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This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
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without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
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GNU General Public License for more details. You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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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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*/
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#include "main.h"
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/*
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//-----------------------------------------------
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// Fast arctan2 with max error of .07 rads
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// http://www.dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm
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//-----------------------------------------------
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signed int arctan_f(signed int x, signed int y)
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{  
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        float rad,r;
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        short int m;
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        #define coeff_1         0.7854
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        #define coeff_2         2.3562
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        #define rad2grad        57.2958  
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   if (!x && !y) return 0;
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   if (y < 0) {y = abs(y); m = -1;}
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   else m = 1;
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   if (x>=0)
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   {
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      r = (float)(x - y) / (float)(x + y);
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      rad = coeff_1 - coeff_1*r;
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   }
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   else
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   {
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      r = (float)(x + y) / (float)(y - x);
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      rad = coeff_2 - coeff_1*r;
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   }
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   rad *= rad2grad;
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   return(rad*m);
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}
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*/
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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};
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signed int arctan_i(signed int x,  signed int y)
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{
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        int i,angle;
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        int8_t m;
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        if (!x && !y) return 0;         //atan2 = 0 für x und y = 0
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        if (y < 0) m=-1;
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        else m=1;
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        if (x==0) return (90*m);                // atan2 = 90° für x = 0
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        i = abs(((float)y / x) * 50.0);         // Berechne i für die Lookup table (Schrittweite atan(x) ist 0.02 -> *50)
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        if (i<270) angle = pgm_read_byte(&pgm_atan[i]); // Lookup für 1° bis 79°
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        else if (i>5750) angle = 90;                                            // Grenzwert ist 90°
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        else if (i>=1910) angle = 89;                                           // 89° bis 80° über Wertebereiche
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        else if (i>=1150) angle = 88;
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        else if (i>=820) angle = 87;
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        else if (i>=640) angle = 86;
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        else if (i>=520) angle = 85;
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        else if (i>=440) angle = 84;
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        else if (i>=380) angle = 83;
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        else if (i>=335) angle = 82;
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        else if (i>=299) angle = 81;
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        else angle = 80; // (i>=270)
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        if (x > 0) return (angle*m);    // Quadrant I und IV
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        else if ((x < 0) && (y >= 0)) return ((angle*-1) + 180);        // Quadrant II
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        else return (angle - 180); // x < 0 && y < 0    Quadrant III
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}
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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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90 
inline float pgm_read_float(const float *addr)
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{      
92 
        union
93 
        {
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                uint16_t i[2];  // 2 16-bit-Worte
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                float f;
96 
        } u;
97 
 
98 
        u.i[0]=pgm_read_word((PGM_P)addr);
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        u.i[1]=pgm_read_word((PGM_P)addr+2);
100 
 
101 
        return u.f;
102 
}
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104 
// cosinus Funktion: Eingabewert Winkel in Grad
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float cos_f(signed int winkel)
106 
{
107 
 return (sin_f(90-winkel));
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}
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// sinus Funktion: Eingabewert Winkel in Grad
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float sin_f(signed int winkel)
205 Nick666 112 
{
113 
 short int m,n;
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 float sinus;
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116 
 //winkel = winkel % 360;
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118 
 if (winkel < 0)
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 {
120 
        m = -1;
121 
        winkel = abs(winkel);
122 
 }
123 
 else m = +1;
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125 
 // Quadranten auswerten
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 if ((winkel > 90 ) && (winkel <= 180)) {winkel = 180 - winkel; n = 1;}
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 else if ((winkel > 180 ) && (winkel <= 270)) {winkel = winkel - 180; n = -1;}
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 else if ((winkel > 270) && (winkel <= 360)) {winkel = 360 - winkel; n = -1;}
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 else n = 1; //0 - 90 Grad
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sinus = pgm_read_float(&pgm_sinus_f[winkel]);
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return (sinus*m*n);
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}
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232 Nick666 137 
/*
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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};
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141 
// cosinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =cos(winkel)*1000
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signed int cos_i(signed int winkel)
143 
{
144 
  return (sin_i(90-winkel));
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}
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// sinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =sin(winkel)*1000
148 
signed int sin_i(signed int winkel)
226 Nick666 149 
{
150 
 short int m,n;
151 
 
152 
 //winkel = winkel % 360;
153 
 
154 
 if (winkel < 0)
155 
 {
156 
        m = -1;
157 
        winkel = abs(winkel);
158 
 }
159 
 else m = +1;
160 
 
161 
 // Quadranten auswerten
162 
 if ((winkel > 90 ) && (winkel <= 180)) {winkel = 180 - winkel; n = 1;}
163 
 else if ((winkel > 180 ) && (winkel <= 270)) {winkel = winkel - 180; n = -1;}
164 
 else if ((winkel > 270) && (winkel <= 360)) {winkel = 360 - winkel; n = -1;}
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 else n = 1; //0 - 90 Grad
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winkel = pgm_read_word(&pgm_sinus[winkel]);
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return (winkel*m*n);
226 Nick666 170 
}
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*/