Revision 1602
Added some test files for fixed point math.
Something definitely broke in cosine when I changed to smaller tables
(which shouldn't have sacrificed any accuracy). Need to investigate...
| fp_math.c | ||
|---|---|---|
| 9 | 9 |
#define FP_TWO_PI 411775 |
| 10 | 10 |
|
| 11 | 11 |
#define TABLE_LENGTH 64 |
| 12 |
#define TABLE_STEP 1621//.160757
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|
| 13 |
#define EXP_MAGICONSTANT |
|
| 12 |
#define TABLE_STEP 1635//.160757
|
|
| 13 |
#define EXP_MAGICONSTANT 726817 //ln(2^16) * 2^16
|
|
| 14 | 14 |
|
| 15 |
//#define DEBUG |
|
| 16 |
|
|
| 17 |
//TODO This can probably be removed at some point. |
|
| 15 | 18 |
static int32_t linspace[TABLE_LENGTH] PROGMEM = {
|
| 16 |
0, 1621, 3242, 4863, 6485, 8106, 9727, 11348,
|
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| 17 |
12969, 14590, 16212, 17833, 19454, 21075, 22696, 24317,
|
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| 18 |
25939, 27560, 29181, 30802, 32423, 34044, 35666, 37287,
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| 19 |
38908, 40529, 42150, 43771, 45393, 47014, 48635, 50256,
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| 20 |
51877, 53498, 55119, 56741, 58362, 59983, 61604, 63225,
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| 21 |
64846, 66468, 68089, 69710, 71331, 72952, 74573, 76195,
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| 22 |
77816, 79437, 81058, 82679, 84300, 85922, 87543, 89164,
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| 23 |
90785, 92406, 94027, 95648, 97270, 98891, 100512, 102133
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| 19 |
0, 1634, 3268, 4902, 6536, 8170, 9804, 11438,
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| 20 |
13072, 14706, 16340, 17974, 19608, 21242, 22876, 24510,
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| 21 |
26144, 27778, 29412, 31047, 32681, 34315, 35949, 37583,
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| 22 |
39217, 40851, 42485, 44119, 45753, 47387, 49021, 50655,
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| 23 |
52289, 53923, 55557, 57191, 58825, 60459, 62093, 63727,
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| 24 |
65361, 66995, 68629, 70263, 71897, 73531, 75165, 76799,
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| 25 |
78433, 80067, 81701, 83335, 84969, 86603, 88237, 89871,
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| 26 |
91506, 93140, 94774, 96408, 98042, 99676, 101310, 102944,
|
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| 24 | 27 |
}; |
| 25 | 28 |
|
| 26 | 29 |
static int32_t fp_cos_table[TABLE_LENGTH] PROGMEM = {
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| 27 |
65536, 65516, 65456, 65356, 65215, 65035, 64815, 64556,
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| 28 |
64257, 63919, 63541, 63125, 62670, 62176, 61645, 61076,
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| 29 |
60470, 59826, 59146, 58430, 57678, 56890, 56068, 55212,
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| 30 |
54322, 53398, 52442, 51454, 50434, 49384, 48303, 47193,
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| 31 |
46053, 44886, 43691, 42470, 41222, 39949, 38652, 37331,
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| 32 |
35988, 34622, 33235, 31828, 30401, 28956, 27492, 26013,
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| 33 |
24517, 23006, 21481, 19943, 18393, 16831, 15260, 13679,
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| 34 |
12089, 10492, 8889, 7280, 5667, 4050, 2431, 811
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| 30 |
65536, 65516, 65455, 65353, 65210, 65027, 64804, 64540,
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| 31 |
64237, 63893, 63509, 63087, 62624, 62123, 61584, 61006,
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| 32 |
60390, 59736, 59046, 58319, 57555, 56756, 55921, 55052,
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| 33 |
54148, 53211, 52241, 51238, 50203, 49138, 48041, 46915,
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| 34 |
45760, 44576, 43364, 42126, 40861, 39571, 38256, 36918,
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| 35 |
35556, 34173, 32768, 31343, 29898, 28435, 26954, 25456,
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| 36 |
23943, 22415, 20872, 19317, 17750, 16171, 14583, 12986,
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| 37 |
11380, 9768, 8149, 6525, 4898, 3267, 1634, 0,
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| 35 | 38 |
}; |
| 36 | 39 |
|
| 37 | 40 |
//FIXME Lazy implementations of tangent and sine. |
| ... | ... | |
| 48 | 51 |
int32_t xsquare = fp_mult(x,x); |
| 49 | 52 |
int32_t result, i; |
| 50 | 53 |
|
| 51 |
if(theta > EXP_MAGICONSTANT) {
|
|
| 54 |
if(x > EXP_MAGICONSTANT) {
|
|
| 52 | 55 |
usb_puts("Output value is out of range.\n\r");
|
| 53 | 56 |
return -1; |
| 54 | 57 |
} |
| 55 | 58 |
|
| 56 | 59 |
//This is again, massive amounts of lazyness. |
| 57 | 60 |
//The approximation fails outside this range (approximately). |
| 58 |
if(theta < -17)
|
|
| 61 |
if(x < (-17l << 16))
|
|
| 59 | 62 |
return 0; |
| 60 | 63 |
|
| 61 | 64 |
result = xsquare; |
| 62 |
for(i= (22 << 16); i > (2 << 16); i-= (4 << 16)) {
|
|
| 65 |
for(i= (22l << 16); i > (2l << 16); i-= (4l << 16)) {
|
|
| 63 | 66 |
result += i; |
| 64 | 67 |
result = fp_div(xsquare, result); |
| 65 | 68 |
} |
| 66 | 69 |
|
| 67 |
result += (2 << 16) - x; |
|
| 68 |
return (1 << 16) + fp_div(fp_mult((2 << 16), x), result);
|
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| 70 |
result += (2l << 16) - x;
|
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| 71 |
return (1l << 16) + fp_div(fp_mult((2l << 16), x), result);
|
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| 69 | 72 |
|
| 70 | 73 |
} |
| 71 | 74 |
|
| ... | ... | |
| 76 | 79 |
int32_t x_n, x_np1, x_np2; |
| 77 | 80 |
int32_t y_n, y_np1, y_np2; |
| 78 | 81 |
int32_t dd_n, dd_np1, second_dd, result; |
| 79 |
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| 82 |
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| 83 |
#ifdef DEBUG |
|
| 84 |
char buf[128]; |
|
| 85 |
#endif |
|
| 86 |
|
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| 80 | 87 |
//Move theta into [0, pi/2] w/ appropriate sign. |
| 81 | 88 |
theta = ABS(theta) % FP_TWO_PI; |
| 82 | 89 |
|
| ... | ... | |
| 90 | 97 |
|
| 91 | 98 |
//Find the nearest table values. FIXME |
| 92 | 99 |
n = theta / TABLE_STEP; |
| 93 |
while( n < TABLE_LENGTH - 1 && (x_np1 = pgm_read_dword(&linspace[n+1]))) |
|
| 100 |
while( n < TABLE_LENGTH - 1 |
|
| 101 |
&& (x_np1 = pgm_read_dword(&linspace[n+1]) < theta)) |
|
| 94 | 102 |
n++; |
| 95 | 103 |
|
| 96 | 104 |
//theta is between x_{n} and x_{n+1}
|
| 105 |
|
|
| 97 | 106 |
if(n == TABLE_LENGTH - 1) {
|
| 98 | 107 |
//Perform linear interpolation, since we're close to zero anyway. |
| 99 | 108 |
x_n = pgm_read_dword(&linspace[TABLE_LENGTH - 1]); |
| 100 | 109 |
y_n = pgm_read_dword(&fp_cos_table[TABLE_LENGTH - 1]); |
| 101 | 110 |
|
| 102 |
result = fp_mult(fp_div(FP_PI_OVER_TWO - x_n, 0 - y_n), theta - x_n) + y_n; |
|
| 111 |
result = fp_mult( |
|
| 112 |
fp_div(FP_PI_OVER_TWO - x_n, 0 - y_n), theta - x_n) + y_n; |
|
| 113 |
|
|
| 103 | 114 |
return negative ? -result : result; |
| 104 | 115 |
} |
| 105 | 116 |
|
| 106 | 117 |
if(n == TABLE_LENGTH) {
|
| 107 | 118 |
//We didn't find a value! Oh no! |
| 108 |
usb_puts("fp_math: We couldn't find surrounding table values! \n\r
|
|
| 109 |
This should never happen!!!\n\r\n\r"); |
|
| 119 |
usb_puts("fp_math: Fatal! We couldn't find surrounding table values! \n\r");
|
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| 120 |
|
|
| 110 | 121 |
return 0; |
| 111 | 122 |
} |
| 112 |
|
|
| 123 |
|
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| 113 | 124 |
//Address the general case. Quadratic interpolation. |
| 114 | 125 |
//Load in the necessary values. |
| 115 | 126 |
x_n = pgm_read_dword(&linspace[n]); |
| 127 |
x_np1 = pgm_read_dword(&linspace[n + 1]); |
|
| 116 | 128 |
x_np2 = pgm_read_dword(&linspace[n + 2]); |
| 117 | 129 |
|
| 118 | 130 |
y_n = pgm_read_dword(&fp_cos_table[n]); |
| 119 | 131 |
y_np1 = pgm_read_dword(&fp_cos_table[n + 1]); |
| 120 | 132 |
y_np2 = pgm_read_dword(&fp_cos_table[n + 2]); |
| 121 | 133 |
|
| 134 |
#ifdef DEBUG |
|
| 135 |
sprintf(buf, "x_n = %ld, theta = %ld, x_{n+1} = %ld", x_n, theta, x_np1);
|
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| 136 |
usb_puts(buf); |
|
| 137 |
#endif |
|
| 138 |
|
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| 122 | 139 |
//Calculate first divided differences. |
| 123 | 140 |
dd_n = fp_div(y_np1 - y_n, x_np1 - x_n); |
| 124 | 141 |
dd_np1 = fp_div(y_np2 - y_np1, x_np2 - x_np1); |
Also available in: Unified diff