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/*
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 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 General Public License for more details. You should have received a copy of the GNU 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"
//-----------------------------------------------
// Fast arctan2 with max error of .07 rads
// http://www.dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm
//-----------------------------------------------
signed int arctan_f
(signed int x
, signed int y
)
{
float rad
,r
;
short int m
;
#define coeff_1 0.7854
#define coeff_2 2.3562
#define rad2grad 57.2958
if (!x
&& !y
) return 0;
if (y
< 0) {y
= abs(y
); m
= -1;}
else m
= 1;
if (x
>=0)
{
r
= (float)(x
- y
) / (float)(x
+ y
);
rad
= coeff_1
- coeff_1
*r
;
}
else
{
r
= (float)(x
+ y
) / (float)(y
- x
);
rad
= coeff_2
- coeff_1
*r
;
}
rad
*= rad2grad
;
return(rad
*m
);
}
/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Peter Muehlenbrock
arctan in brute-force Art
Stand 1.10.2007
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
*/
// arctan Funktion: Eingabewert x,y Rueckgabe =arctan(x,y) in grad
signed int arctan_i
(signed int x
, signed int y
)
{
short int change_xy
= 0;
signed int i
;
long signed int wert
;
int return_value
;
if ((abs(x
)) > (abs(y
))) // x,y Werte vertauschen damit arctan <45 grad bleibt
{
change_xy
= 1;
i
= x
;
x
= y
;
y
= i
;
}
// Quadranten ermitteln
// Wert durch lineare Interpolation ermitteln
if (!y
&& !x
) return 0; // Division durch 0 nicht erlaubt
else wert
= abs((x
*1000)/y
);
if (wert
<=268) //0...0.0,268 entsprechend 0..15 Grad
{
return_value
= (signed int)((wert
*100)/(268-0)*(15-0)/100) +0;
}
else if (wert
<=578) //0,268...0.0,568 entsprechend 15..30 Grad
{
return_value
= (signed int)((((wert
-268)*100)/(578-268)*(30-15))/100) +15;
}
else //0,568...1 entsprechend 30..45 Grad
{
return_value
= (signed int)((((wert
-578)*50)/(1000-578)*(45-30))/50) +30;
}
if (change_xy
== 0) return_value
= 90-return_value
; //Quadrant 45..90 Grad
if ((x
>= 0) && (y
<0)) return_value
= - return_value
;
else if ((x
< 0) && (y
>= 0)) return_value
= - return_value
;
return return_value
;
}
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;
}
// cosinus Funktion: Eingabewert Winkel in Grad
float cos_f
(signed int winkel
)
{
return (sin_f
(90-winkel
));
}
// sinus Funktion: Eingabewert Winkel in Grad
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 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};
// cosinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =cos(winkel)*1000
signed int cos_i
(signed int winkel
)
{
return (sin_i
(90-winkel
));
}
// sinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =sin(winkel)*1000
signed int sin_i
(signed int winkel
)
{
short int m
,n
;
//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
winkel
= pgm_read_word
(&pgm_sinus
[winkel
]);
return (winkel
*m
*n
);
}