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/*
Copyright 2007, Niklas Nold
This program (files math.c and math.h) is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation;
either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
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
*/
#include "main.h"
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};
// Arkustangens2 im Gradmaß
signed int atan2_i
(signed int x
, signed int y
)
{
int i
,angle
;
int8_t m
;
if (!x
&& !y
) return 0; //atan2 = 0 für x und y = 0
if (y
< 0) m
=-1;
else m
=1;
if (x
==0) return (90*m
); // atan2 = 90° für x = 0
i
= abs(((float)y
/ x
) * 50); // Berechne i für die Lookup table (Schrittweite atan(x) ist 0.02 -> *50)
if (i
<270) angle
= pgm_read_byte
(&pgm_atan
[i
]); // Lookup für 1° bis 79°
else if (i
>5750) angle
= 90; // Grenzwert ist 90°
else if (i
>=1910) angle
= 89; // 89° bis 80° über Wertebereiche
else if (i
>=1150) angle
= 88;
else if (i
>=820) angle
= 87;
else if (i
>=640) angle
= 86;
else if (i
>=520) angle
= 85;
else if (i
>=440) angle
= 84;
else if (i
>=380) angle
= 83;
else if (i
>=335) angle
= 82;
else if (i
>=299) angle
= 81;
else angle
= 80; // (i>=270)
if (x
> 0) return (angle
*m
); // Quadrant I und IV
else if ((x
< 0) && (y
>= 0)) return ((angle
*-1) + 180); // Quadrant II
else return (angle
- 180); // x < 0 && y < 0 Quadrant III
}
//Sinusfunktion von 0° bis 359°. Ergebnis wurde mit 1000 multipliziert, damit als Definition platzsparend int
//verwendet werden kann. d.h., es muss also in der späteren Berechnung noch mit 0,001 multipliziert werden //(090907Kr)
const int c_sin
[] = {0,17,34,52,69,87,104,121,139,156,173,190,
207,224,241,258,275,292,309,325,342,358,374,390,406,422,438,453,469,484,500,515,529,544,559,573,587,601,615,629,
642,656,669,682,694,707,719,731,743,754,766,777,788,798,809,819,829,838,848,857,866,874,882,891,898,906,913,920,
927,933,939,945,951,956,961,965,970,974,978,981,984,987,990,992,994,996,997,998,999,999,1000,999,999,998,997,996,
994,992,990,987,984,981,978,974,970,965,961,956,951,945,939,933,927,920,913,906,898,891,882,874,866,857,848,838,
829,819,809,798,788,777,766,754,743,731,719,707,694,682,669,656,642,629,615,601,587,573,559,544,529,515,500,484,
469,453,438,422,406,390,374,358,342,325,309,292,275,258,241,224,207,190,173,156,139,121,104,87,69,52,34,17,0,-17,
-34,-52,-69,-87,-104,-121,-139,-156,-173,-190,-207,-224,-241,-258,-275,-292,-309,-325,-342,-358,-374,-390,-406,
-422,-438,-453,-469,-484,-500,-515,-529,-544,-559,-573,-587,-601,-615,-629,-642,-656,-669,-682,-694,-707,-719,
-731,-743,-754,-766,-777,-788,-798,-809,-819,-829,-838,-848,-857,-866,-874,-882,-891,-898,-906,-913,-920,-927,
-933,-939,-945,-951,-956,-961,-965,-970,-974,-978,-981,-984,-987,-990,-992,-994,-996,-997,-998,-999,-999,-1000,
-999,-999,-998,-997,-996,-994,-992,-990,-987,-984,-981,-978,-974,-970,-965,-961,-956,-951,-945,-939,-933,-927,
-920,-913,-906,-898,-891,-882,-874,-866,-857,-848,-838,-829,-819,-809,-798,-788,-777,-766,-754,-743,-731,-719,
-707,-694,-682,-669,-656,-642,-629,-615,-601,-587,-573,-559,-544,-529,-515,-500,-484,-469,-453,-438,-422,-406,
-390,-374,-358,-342,-325,-309,-292,-275,-258,-241,-224,-207,-190,-173,-156,-139,-121,-104,-87,-69,-52,-34,-17};
//Cosinusfunktion von 0° bis 359°. Ergebnis wurde mit 1000 multipliziert, damit als Definition platzsparend int
//verwendet werden kann. D.h., es muss also in der späteren Berechnung noch mit 0,001 multipliziert werden //(090907Kr)
const int c_cos
[] = {1000,999,999,998,997,996,994,992,990,987,984,981,
978,974,970,965,961,956,951,945,939,933,927,920,913,906,898,891,882,874,866,857,848,838,829,819,809,798,788,777,
766,754,743,731,719,707,694,682,669,656,642,629,615,601,587,573,559,544,529,515,500,484,469,453,438,422,406,390,
374,358,342,325,309,292,275,258,241,224,207,190,173,156,139,121,104,87,69,52,34,17,0,-17,-34,-52,-69,-87,-104,
-121,-139,-156,-173,-190,-207,-224,-241,-258,-275,-292,-309,-325,-342,-358,-374,-390,-406,-422,-438,-453,-469,
-484,-500,-515,-529,-544,-559,-573,-587,-601,-615,-629,-642,-656,-669,-682,-694,-707,-719,-731,-743,-754,-766,
-777,-788,-798,-809,-819,-829,-838,-848,-857,-866,-874,-882,-891,-898,-906,-913,-920,-927,-933,-939,-945,-951,
-956,-961,-965,-970,-974,-978,-981,-984,-987,-990,-992,-994,-996,-997,-998,-999,-999,-1000,-999,-999,-998,-997,
-996,-994,-992,-990,-987,-984,-981,-978,-974,-970,-965,-961,-956,-951,-945,-939,-933,-927,-920,-913,-906,-898,
-891,-882,-874,-866,-857,-848,-838,-829,-819,-809,-798,-788,-777,-766,-754,-743,-731,-719,-707,-694,-682,-669,
-656,-642,-629,-615,-601,-587,-573,-559,-544,-529,-515,-500,-484,-469,-453,-438,-422,-406,-390,-374,-358,-342,
-325,-309,-292,-275,-258,-241,-224,-207,-190,-173,-156,-139,-121,-104,-87,-69,-52,-34,-17,0,17,34,52,69,87,
104,121,139,156,173,190,207,224,241,258,275,292,309,325,342,358,374,390,406,422,438,453,469,484,500,515,529,544,
559,573,587,601,615,629,642,656,669,682,694,707,719,731,743,754,766,777,788,798,809,819,829,838,848,857,866,874,
882,891,898,906,913,920,927,933,939,945,951,956,961,965,970,974,978,981,984,987,990,992,994,996,997,998,999,999};
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};
inline float pgm_read_float
(const float *addr
)
{
union
{
uint16_t i
[2]; // 2 16-bit-Worte
float f
;
} u
;
u.
i[0]=pgm_read_word
((PGM_P
)addr
);
u.
i[1]=pgm_read_word
((PGM_P
)addr
+2);
return u.
f;
}
// Kosinusfunktion im Gradmaß
float cos_f
(signed int winkel
)
{
return (sin_f
(90-winkel
));
}
// Sinusfunktion im Gradmaß
float sin_f
(signed int winkel
)
{
short int m
,n
;
float sinus
;
//winkel = winkel % 360;
if (winkel
< 0)
{
m
= -1;
winkel
= abs(winkel
);
}
else m
= +1;
// Quadranten auswerten
if ((winkel
> 90 ) && (winkel
<= 180))
{winkel
= 180 - winkel
; n
= 1;}
else if ((winkel
> 180 ) && (winkel
<= 270))
{winkel
= winkel
- 180; n
= -1;}
else if ((winkel
> 270) && (winkel
<= 360))
{winkel
= 360 - winkel
; n
= -1;}
else
n
= 1; //0 - 90 Grad
sinus
= pgm_read_float
(&pgm_sinus_f
[winkel
]);
return (sinus
*m
*n
);
}
const uint8_t pgm_asin
[201] PROGMEM
= {0,0,1,1,1,1,2,2,2,3,3,3,3,4,4,4,5,5,5,5,6,
6,6,7,7,7,7,8,8,8,9,9,9,9,10,10,10,11,11,11,12,12,12,12,13,13,13,14,14,14,14,15,
15,15,16,16,16,17,17,17,17,18,18,18,19,19,19,20,20,20,20,21,21,21,22,22,22,23,23,
23,24,24,24,25,25,25,25,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,31,31,31,32,
32,32,33,33,33,34,34,34,35,35,35,36,36,37,37,37,38,38,38,39,39,39,40,40,41,41,41,
42,42,42,43,43,44,44,44,45,45,46,46,46,47,47,48,48,49,49,49,50,50,51,51,52,52,53,
53,54,54,55,55,56,56,57,57,58,58,59,59,60,60,61,62,62,63,64,64,65,66,66,67,68,68,
69,70,71,72,73,74,75,76,77,79,80,82,84,90};
// Akurssinusfunktion im Gradmaß
int8_t asin_i
(signed int i
)
{
signed char m
;
if (i
< 0) {m
=-1;i
=abs(i
);}
else m
=1;
return (pgm_read_byte
(&pgm_asin
[i
]) * m
);
}