Revision 1585
Cut the trig table sizes in 4 w/ symmetry, etc.
Lazy implementations of sine and tangent (that just
use cosine indirectly).
Addressed edge cases.
Needs EXTENSIVE testing to get a good grip on error bounds.
| trunk/code/projects/fp_math/fp_math.c | ||
|---|---|---|
| 5 | 5 |
#include <serial.h> |
| 6 | 6 |
|
| 7 | 7 |
#define ABS(x) (x > 0 ? x : -x) |
| 8 |
#define FP_PI_OVER_TWO 102944 |
|
| 9 |
#define FP_TWO_PI 411775 |
|
| 8 | 10 |
|
| 9 |
#define TABLE_LENGTH 128
|
|
| 11 |
#define TABLE_LENGTH 64
|
|
| 10 | 12 |
#define TABLE_STEP 1621//.160757 |
| 11 | 13 |
|
| 14 |
static inline int32_t trig_lookup(int32_t theta, int32_t* table); |
|
| 15 |
|
|
| 12 | 16 |
static int32_t linspace[TABLE_LENGTH] PROGMEM = {
|
| 13 | 17 |
0, 1621, 3242, 4863, 6485, 8106, 9727, 11348, |
| 14 | 18 |
12969, 14590, 16212, 17833, 19454, 21075, 22696, 24317, |
| ... | ... | |
| 17 | 21 |
51877, 53498, 55119, 56741, 58362, 59983, 61604, 63225, |
| 18 | 22 |
64846, 66468, 68089, 69710, 71331, 72952, 74573, 76195, |
| 19 | 23 |
77816, 79437, 81058, 82679, 84300, 85922, 87543, 89164, |
| 20 |
90785, 92406, 94027, 95648, 97270, 98891, 100512, 102133, |
|
| 21 |
103754, 105375, 106997, 108618, 110239, 111860, 113481, 115102, |
|
| 22 |
116724, 118345, 119966, 121587, 123208, 124829, 126451, 128072, |
|
| 23 |
129693, 131314, 132935, 134556, 136178, 137799, 139420, 141041, |
|
| 24 |
142662, 144283, 145904, 147526, 149147, 150768, 152389, 154010, |
|
| 25 |
155631, 157253, 158874, 160495, 162116, 163737, 165358, 166980, |
|
| 26 |
168601, 170222, 171843, 173464, 175085, 176707, 178328, 179949, |
|
| 27 |
181570, 183191, 184812, 186433, 188055, 189676, 191297, 192918, |
|
| 28 |
194539, 196160, 197782, 199403, 201024, 202645, 204266, 205887 |
|
| 24 |
90785, 92406, 94027, 95648, 97270, 98891, 100512, 102133 |
|
| 29 | 25 |
}; |
| 30 | 26 |
|
| 31 |
static int32_t cos_table[TABLE_LENGTH] PROGMEM = {
|
|
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static int32_t fp_cos_table[TABLE_LENGTH] PROGMEM = {
|
|
| 32 | 28 |
65536, 65516, 65456, 65356, 65215, 65035, 64815, 64556, |
| 33 | 29 |
64257, 63919, 63541, 63125, 62670, 62176, 61645, 61076, |
| 34 | 30 |
60470, 59826, 59146, 58430, 57678, 56890, 56068, 55212, |
| ... | ... | |
| 36 | 32 |
46053, 44886, 43691, 42470, 41222, 39949, 38652, 37331, |
| 37 | 33 |
35988, 34622, 33235, 31828, 30401, 28956, 27492, 26013, |
| 38 | 34 |
24517, 23006, 21481, 19943, 18393, 16831, 15260, 13679, |
| 39 |
12089, 10492, 8889, 7280, 5667, 4050, 2431, 811, |
|
| 40 |
-811, -2431, -4050, -5667, -7280, -8889, -10492, -12089, |
|
| 41 |
-13679, -15260, -16831, -18393, -19943, -21481, -23006, -24517, |
|
| 42 |
-26013, -27492, -28956, -30401, -31828, -33235, -34622, -35988, |
|
| 43 |
-37331, -38652, -39949, -41222, -42470, -43691, -44886, -46053, |
|
| 44 |
-47193, -48303, -49384, -50434, -51454, -52442, -53398, -54322, |
|
| 45 |
-55212, -56068, -56890, -57678, -58430, -59146, -59826, -60470, |
|
| 46 |
-61076, -61645, -62176, -62670, -63125, -63541, -63919, -64257, |
|
| 47 |
-64556, -64815, -65035, -65215, -65356, -65456, -65516, -65536 |
|
| 35 |
12089, 10492, 8889, 7280, 5667, 4050, 2431, 811 |
|
| 48 | 36 |
}; |
| 49 | 37 |
|
| 50 |
static int32_t sin_table[TABLE_LENGTH] PROGMEM = {
|
|
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0, 1621, 3241, 4859, 6474, 8085, 9691, 11292, |
|
| 52 |
12885, 14470, 16047, 17614, 19169, 20714, 22245, 23763, |
|
| 53 |
25267, 26755, 28226, 29680, 31117, 32534, 33931, 35307, |
|
| 54 |
36662, 37995, 39304, 40589, 41849, 43084, 44292, 45473, |
|
| 55 |
46627, 47751, 48847, 49913, 50948, 51952, 52924, 53864, |
|
| 56 |
54771, 55644, 56484, 57288, 58058, 58792, 59491, 60152, |
|
| 57 |
60777, 61365, 61915, 62428, 62902, 63338, 63735, 64093, |
|
| 58 |
64411, 64691, 64930, 65130, 65291, 65411, 65491, 65531, |
|
| 59 |
65531, 65491, 65411, 65291, 65130, 64930, 64691, 64411, |
|
| 60 |
64093, 63735, 63338, 62902, 62428, 61915, 61365, 60777, |
|
| 61 |
60152, 59491, 58792, 58058, 57288, 56484, 55644, 54771, |
|
| 62 |
53864, 52924, 51952, 50948, 49913, 48847, 47751, 46627, |
|
| 63 |
45473, 44292, 43084, 41849, 40589, 39304, 37995, 36662, |
|
| 64 |
35307, 33931, 32534, 31117, 29680, 28226, 26755, 25267, |
|
| 65 |
23763, 22245, 20714, 19169, 17614, 16047, 14470, 12885, |
|
| 66 |
11292, 9691, 8085, 6474, 4859, 3241, 1621, 0 |
|
| 67 |
}; |
|
| 38 |
//FIXME Lazy implementations of tangent and sine. |
|
| 39 |
int32_t fp_tan(int32_t theta) {
|
|
| 40 |
return fp_div(fp_sin(theta), fp_cos(theta)); |
|
| 41 |
} |
|
| 68 | 42 |
|
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int32_t fp_sin(int32_t theta) {
|
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return fp_cos(theta + FP_PI_OVER_TWO); |
|
| 45 |
} |
|
| 46 |
|
|
| 69 | 47 |
//Quadratic interpolation. |
| 70 | 48 |
int32_t fp_cos(int32_t theta) {
|
| 71 | 49 |
uint8_t n; |
| 50 |
int8_t negative; |
|
| 72 | 51 |
int32_t x_n, x_np1, x_np2; |
| 73 | 52 |
int32_t y_n, y_np1, y_np2; |
| 74 |
int32_t dd_n, dd_np1, second_dd; |
|
| 53 |
int32_t dd_n, dd_np1, second_dd, result;
|
|
| 75 | 54 |
|
| 76 |
//Move theta into [0, pi] |
|
| 77 |
theta = ABS(theta) % FP_TWO_PI; |
|
| 55 |
//Move theta into [0, pi/2] w/ appropriate sign. |
|
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theta = ABS(theta) % FP_TWO_PI; |
|
| 57 |
|
|
| 78 | 58 |
if(theta > FP_PI) |
| 79 | 59 |
theta = FP_TWO_PI - theta; |
| 60 |
|
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| 61 |
if(theta > FP_PI_OVER_TWO) {
|
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theta = FP_PI - theta; |
|
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negative = 1; |
|
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} |
|
| 80 | 65 |
|
| 81 | 66 |
//Find the nearest table values. FIXME |
| 82 | 67 |
n = theta / TABLE_STEP; |
| 83 |
while((x_np1 = pgm_read_dword(&linspace[n+1])) < theta) n++;
|
|
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usb_puti(n);
|
|
| 68 |
while( n < TABLE_LENGTH - 1 && (x_np1 = pgm_read_dword(&linspace[n+1])))
|
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n++;
|
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| 85 | 70 |
|
| 86 | 71 |
//theta is between x_{n} and x_{n+1}
|
| 87 |
|
|
| 88 |
//Address edge cases. |
|
| 89 |
if(n == 0) {
|
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| 90 |
//TODO |
|
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} |
|
| 92 | 72 |
|
| 93 | 73 |
if(n == TABLE_LENGTH - 1) {
|
| 94 |
//TODO |
|
| 74 |
//Perform linear interpolation, since we're close to zero anyway. |
|
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x_n = pgm_read_dword(&linspace[TABLE_LENGTH - 1]); |
|
| 76 |
y_n = pgm_read_dword(&fp_cos_table[TABLE_LENGTH - 1]); |
|
| 77 |
|
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| 78 |
result = fp_mult(fp_div(FP_PI_OVER_TWO - x_n, 0 - y_n), theta - x_n) + y_n; |
|
| 79 |
return negative ? -result : result; |
|
| 95 | 80 |
} |
| 81 |
|
|
| 82 |
if(n == TABLE_LENGTH) {
|
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| 83 |
//We didn't find a value! Oh no! |
|
| 84 |
usb_puts("fp_math: We couldn't find surrounding table values! \n\r
|
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| 85 |
This should never happen!!!\n\r\n\r"); |
|
| 86 |
return 0; |
|
| 87 |
} |
|
| 96 | 88 |
|
| 97 | 89 |
//Address the general case. Quadratic interpolation. |
| 98 | 90 |
//Load in the necessary values. |
| 99 | 91 |
x_n = pgm_read_dword(&linspace[n]); |
| 100 |
x_np1 = pgm_read_dword(&linspace[n + 1]); |
|
| 101 | 92 |
x_np2 = pgm_read_dword(&linspace[n + 2]); |
| 102 | 93 |
|
| 103 |
y_n = pgm_read_dword(&cos_table[n]); |
|
| 104 |
y_np1 = pgm_read_dword(&cos_table[n + 1]); |
|
| 105 |
y_np2 = pgm_read_dword(&cos_table[n + 2]); |
|
| 94 |
y_n = pgm_read_dword(&fp_cos_table[n]);
|
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| 95 |
y_np1 = pgm_read_dword(&fp_cos_table[n + 1]);
|
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| 96 |
y_np2 = pgm_read_dword(&fp_cos_table[n + 2]);
|
|
| 106 | 97 |
|
| 107 | 98 |
//Calculate first divided differences. |
| 108 | 99 |
dd_n = fp_div(y_np1 - y_n, x_np1 - x_n); |
| ... | ... | |
| 111 | 102 |
//Calculate the second divided difference. |
| 112 | 103 |
second_dd = fp_div(dd_np1 - dd_n, x_np2 - x_n); |
| 113 | 104 |
|
| 114 |
return fp_mult(fp_mult(second_dd, theta - x_n), theta - x_np1) |
|
| 115 |
+ fp_mult(dd_n, theta - x_n) + y_n; |
|
| 105 |
result = fp_mult(fp_mult(second_dd, theta - x_n), theta - x_np1) |
|
| 106 |
+ fp_mult(dd_n, theta - x_n) + y_n; |
|
| 107 |
|
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| 108 |
return negative ? -result : result; |
|
| 116 | 109 |
} |
| 117 | 110 |
|
| 118 | 111 |
//FIXME I didn't write these functions very carefully... |
| trunk/code/projects/fp_math/fp_math.h | ||
|---|---|---|
| 3 | 3 |
#define _FP_MATH_H_ |
| 4 | 4 |
|
| 5 | 5 |
#define FP_PI 205887 |
| 6 |
#define FP_TWO_PI 411775 |
|
| 7 | 6 |
|
| 8 | 7 |
#include <stdint.h> |
| 9 | 8 |
|
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