## root/modules/cordic_math.h

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## INCLUDED FROM

```   1 /*
2 CORDIC LIBRARY
3 integer based trigonometric mathematics
4 all values scaled by 100000 (CORDIC_SCALE)
5
7
8 (c)2012/2013 rudi from CHDK[-DE] forum
10
11 trigonometric functions
12     angle as DEG:
13     sind, cosd, tand, asind, acosd, atand, recd, pold
15     sinr, cosr, tanr, asinr, acosr, atanr, recr, polr
16
18     integer calculation (a * b / c):
19     fixed muldivScaled(fixed a , fixed b, fixed c)
20
22     fixed fint(a)   get integer
23     fixed fceil(a)  get largest previous integer
24     fixed ffloor(a) get smallest following integer
25     fixed fround(a) get nearest integer
26
27 all values in CORDIC routines are from type 'fixed' (4 byte integer)
28     makros to convert values:
29     FIXED(X) ...... convert double to cordic fixed
30     FLOAT(X) ...... convert cordic fixed to double
31     INT2FIXED(X) .. convert integer (value *1000) to cordic fixed
32     INT2FIXEDR(X) . equal to INT2FIXED(X) with round
33     FIXED2INT(X) .. convert cordic fixed to integer (value * 1000)
34     FIXED2INTR(X) . equal to FIXED2INT(X) with round
35 */
36
37 typedef long fixed;
38 typedef int int4b; //4 byte integer
39 enum fcordic {ROTATE, VECTOR};
40 typedef int fcordic;
42 typedef int tangle;
43
44 enum {
45     FRACTIONBITS = 17,
46     N = 17,
47     M = 9,
48     CORDIC_SCALE = 1 << FRACTIONBITS,
49     CORDIC_INTEGER = ~(CORDIC_SCALE - 1),
50     INT_SCALE = 1000,
51 };
52
53 #include "limits.h"
54
55 #define FIXED(X)        (floatToFixed((X)))
56 #define FLOAT(X)        ((X) / (double)CORDIC_SCALE)
57 #define INT2FIXED(X)    (intToFixed((X), 0))
58 #define INT2FIXEDR(X)   (intToFixed((X), 1))
59 #define FIXED2INT(X)    (fixedToInt((X), 0))
60 #define FIXED2INTR(X)   (fixedToInt((X), 1))
61
62 //intern used functions
63 LUALIB_API void cordic(tangle t, fcordic f, fixed *x, fixed *y, fixed *z);
64 LUALIB_API fixed mulScaled(fixed a, fixed b);
65 LUALIB_API fixed divScaled(fixed a, fixed b);
66 LUALIB_API int convertToQ1(fixed *x, fixed *y);
67 LUALIB_API void convertFromQ1(fixed *x, fixed *y, int q);
68 LUALIB_API int rotateToQ1(tangle t, fixed *phi);
69 LUALIB_API void rotateFromQ1(tangle t, fixed *phi, int q);
70 LUALIB_API fixed cathetus(fixed x);
71 /* base CIRCULAR mode, ROTATE */
72 LUALIB_API void sincosCordic(tangle t, fixed phi, fixed *sinphi, fixed *cosphi);
73 /* base CIRCULAR mode, VECTOR */
74 LUALIB_API void atanhypCordic(tangle t, fixed px, fixed py, fixed *phi, fixed *hyp);
75 /* functions CIRCULAR mode, ROTATE */
76 LUALIB_API fixed sinCordic(tangle t, fixed phi);
77 LUALIB_API fixed cosCordic(tangle t, fixed phi);
78 LUALIB_API fixed tanCordic(tangle t, fixed phi);
79 LUALIB_API void recCordic(tangle t, fixed r, fixed theta, fixed *px, fixed *py);
80 /* functions CIRCULAR mode, VECTOR */
81 LUALIB_API fixed asinCordic(tangle t, fixed x);
82 LUALIB_API fixed acosCordic(tangle t, fixed x);
83 LUALIB_API fixed atanCordic(tangle t, fixed x);
84 LUALIB_API void polCordic(tangle t, fixed px, fixed py, fixed *r, fixed *theta);
85
86 // extern
87 // PI/2, PI, 2*PI
88 LUAI_DATA fixed FULL_CIRCLE[];
89 LUAI_DATA fixed HALF_CIRCLE[];
90 LUAI_DATA fixed QUART_CIRCLE[];
91 //used by macro
92 LUALIB_API fixed floatToFixed(double a);
93 LUALIB_API fixed intToFixed(int4b a, int round);
94 LUALIB_API int4b fixedToInt(fixed a, int round);
96 LUALIB_API fixed muldivScaled(fixed a, fixed b, fixed c);
97 // DEG
98 LUALIB_API fixed sind(fixed phi);
99 LUALIB_API fixed cosd(fixed phi);
100 LUALIB_API fixed tand(fixed phi);
101 LUALIB_API void recd(fixed r, fixed theta, fixed *px, fixed *py);
102 LUALIB_API fixed asind(fixed x);
103 LUALIB_API fixed acosd(fixed x);
104 LUALIB_API fixed atand(fixed x);
105 LUALIB_API void pold(fixed px, fixed py, fixed *r, fixed *theta);
107 LUALIB_API fixed sinr(fixed phi);
108 LUALIB_API fixed cosr(fixed phi);
109 LUALIB_API fixed tanr(fixed phi);
110 LUALIB_API void recr(fixed r, fixed theta, fixed *px, fixed *py);
111 LUALIB_API fixed asinr(fixed x);
112 LUALIB_API fixed acosr(fixed x);
113 LUALIB_API fixed atanr(fixed x);
114 LUALIB_API void polr(fixed px, fixed py, fixed *r, fixed *theta);