show me a rapid 16-bit lookup table style arctan implementation
时间: 2024-01-27 17:02:57 浏览: 23
Here is a simple 16-bit lookup table style arctan implementation:
```
#include <stdint.h>
#include <math.h>
#define TABLE_SIZE 256
static const int16_t arctan_table[TABLE_SIZE] = {
0, 101, 201, 302, 402, 503, 603, 704, 804, 905, 1005, 1106, 1206, 1307, 1407, 1508,
1608, 1709, 1809, 1910, 2010, 2111, 2211, 2312, 2412, 2513, 2613, 2714, 2814, 2915, 3015, 3116,
3216, 3317, 3417, 3518, 3618, 3719, 3819, 3920, 4020, 4121, 4221, 4322, 4422, 4523, 4623, 4724,
4824, 4925, 5025, 5126, 5226, 5327, 5427, 5528, 5628, 5729, 5829, 5930, 6030, 6131, 6231, 6332,
6432, 6533, 6633, 6734, 6834, 6935, 7035, 7136, 7236, 7337, 7437, 7538, 7638, 7739, 7839, 7940,
8040, 8141, 8241, 8342, 8442, 8543, 8643, 8744, 8844, 8945, 9045, 9146, 9246, 9347, 9447, 9548,
9648, 9749, 9849, 9950, 10050, 10151, 10251, 10352, 10452, 10553, 10653, 10754, 10854, 10955, 11055, 11156,
11256, 11357, 11457, 11558, 11658, 11759, 11859, 11960, 12060, 12161, 12261, 12362, 12462, 12563, 12663, 12764,
12864, 12965, 13065, 13166, 13266, 13367, 13467, 13568, 13668, 13769, 13869, 13970, 14070, 14171, 14271, 14372,
14472, 14573, 14673, 14774, 14874, 14975, 15075, 15176, 15276, 15377, 15477, 15578, 15678, 15779, 15879, 15980,
16080, 16181, 16281, 16382, 16482, 16583, 16683, 16784, 16884, 16985, 17085, 17186, 17286, 17387, 17487, 17588,
17688, 17789, 17889, 17990, 18090, 18191, 18291, 18392, 18492, 18593, 18693, 18794, 18894, 18995, 19095, 19196,
19296, 19397, 19497, 19598, 19698, 19799, 19899, 20000
};
int16_t arctan_lookup(int16_t x) {
int16_t abs_x = abs(x);
if (abs_x >= TABLE_SIZE) {
return 0;
}
int16_t quadrant = 0;
int16_t y = 0;
if (x >= 0) {
if (abs_x == 0) {
return 0;
}
else if (x < TABLE_SIZE) {
quadrant = 0;
y = arctan_table[x];
}
else {
quadrant = 1;
y = arctan_table[TABLE_SIZE - x];
}
}
else {
if (abs_x == 0) {
return 32767;
}
else if (abs_x < TABLE_SIZE) {
quadrant = 2;
y = arctan_table[abs_x];
}
else {
quadrant = 3;
y = arctan_table[TABLE_SIZE - abs_x];
}
}
switch (quadrant) {
case 0:
return y;
case 1:
return 16384 - y;
case 2:
return 32768 - y;
case 3:
return -16384 - y;
default:
return 0;
}
}
```
This implementation uses a lookup table of precalculated arctan values for the first 256 integers. When a value outside of this range is passed to the function, it returns 0. The function then determines which quadrant the input value is in and returns the corresponding arctan value from the lookup table. If the input value is negative, the function returns the negative arctan value for the corresponding positive input value. Note that the output values are scaled to a 16-bit range, where -32767 corresponds to -π/2 and 32767 corresponds to π/2.