show me a rapid lookup table style arctan implementation
时间: 2023-07-02 18:11:18 浏览: 52
Here is a sample implementation of a lookup table style arctan function in C++:
```c++
#include <iostream>
#include <cmath>
#define TABLE_SIZE 1000
#define PI 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
double arctan(double x) {
static double arctan_table[TABLE_SIZE + 1];
static bool initialized = false;
// Initialize lookup table
if (!initialized) {
for (int i = 0; i <= TABLE_SIZE; i++) {
arctan_table[i] = std::atan(i / (double)TABLE_SIZE);
}
initialized = true;
}
// Lookup arctan value
if (x >= 0) {
return arctan_table[(int)(x * TABLE_SIZE)];
} else {
return -arctan_table[(int)(-x * TABLE_SIZE)];
}
}
int main() {
std::cout << arctan(0.5) << std::endl;
std::cout << arctan(1) << std::endl;
std::cout << arctan(-0.5) << std::endl;
std::cout << arctan(-1) << std::endl;
std::cout << arctan(0) << std::endl;
std::cout << arctan(PI/4) << std::endl;
return 0;
}
```
This implementation uses a lookup table of precomputed arctan values for evenly spaced points between 0 and 1. The value of arctan for any given input x is then looked up in the table by multiplying x by the table size and rounding down to the nearest integer. For negative values of x, the value is negated before looking up in the table and then negated again before returning. Note that the implementation assumes that the input x is between -1 and 1.