show me a rapid 16-bit arctan implementation
时间: 2024-02-06 07:09:31 浏览: 25
Here's a possible implementation of a rapid 16-bit arctan function using a lookup table and linear interpolation:
```c
#include <stdint.h>
// Constants for the lookup table
#define SIZE 1024
#define PI_OVER_2 16384 // 2^14 * PI/2
#define ATAN_1_OVER_X_MAX 8192 // 2^13
// Lookup table for arctan(1/x)
uint16_t atan_1_over_x[SIZE + 1];
// Initialize the lookup table
void init_atan_1_over_x() {
for (int i = 0; i <= SIZE; i++) {
double x = (double)i / SIZE;
atan_1_over_x[i] = (uint16_t)(atan(1 / x) * PI_OVER_2 / M_PI);
}
}
// Rapid 16-bit arctan function using lookup table and linear interpolation
uint16_t atan16(int16_t x) {
if (x == 0) return 0;
int16_t abs_x = abs(x);
uint16_t index = abs_x >= SIZE ? SIZE : abs_x;
uint16_t y0 = atan_1_over_x[index];
uint16_t y1 = atan_1_over_x[index + 1];
uint16_t dy = y1 - y0;
uint16_t frac = ((uint32_t)(abs_x - index) << 16) / SIZE;
uint16_t y = y0 + frac * dy;
return x > 0 ? PI_OVER_2 - y : y - PI_OVER_2;
}
```
The `init_atan_1_over_x()` function initializes a lookup table for arctan(1/x) values. The function `atan16(x)` takes a 16-bit integer `x` and returns the 16-bit arctan value in radians (scaled by 2^14). The function first looks up the arctan(1/x) value in the table using the absolute value of `x`, linearly interpolates between the two closest table values to get the arctan value for `x`, and then adjusts the sign of the result based on the sign of `x`.
Note that this implementation is not optimized for speed and may not be suitable for real-time applications.