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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
}
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
);
}