c++ – Calculation of the sine function

I have been attempting to implement a function calculating values of the sine function.
I know that there are several similar threads regarding this topic but my goal was to try
to implement such function in my own way as an excercise.

In the time being I have below given code in C++ language which seems to be working (I have
compared the outputs of that code with the sine values calculated by the Excel).

#define PI         3.14
#define TABLE_SIZE 256
#define STEP_SIZE (2*PI/255)

double lut(TABLE_SIZE) = {
    0.0000, 0.0245, 0.0490, 0.0735, 0.0980, 0.1223, 0.1467, 0.1709, 
    0.1950, 0.2190, 0.2429, 0.2666, 0.2901, 0.3135, 0.3367, 0.3597, 
    0.3825, 0.4050, 0.4274, 0.4494, 0.4712, 0.4927, 0.5139, 0.5348, 
    0.5553, 0.5756, 0.5954, 0.6150, 0.6341, 0.6529, 0.6713, 0.6893, 
    0.7068, 0.7240, 0.7407, 0.7569, 0.7727, 0.7881, 0.8029, 0.8173, 
    0.8312, 0.8446, 0.8575, 0.8698, 0.8817, 0.8930, 0.9037, 0.9140, 
    0.9237, 0.9328, 0.9413, 0.9493, 0.9568, 0.9636, 0.9699, 0.9756, 
    0.9806, 0.9852, 0.9891, 0.9924, 0.9951, 0.9972, 0.9988, 0.9997, 
    1.0000, 0.9997, 0.9988, 0.9974, 0.9953, 0.9926, 0.9893, 0.9854, 
    0.9810, 0.9759, 0.9703, 0.9640, 0.9572, 0.9498, 0.9419, 0.9333, 
    0.9243, 0.9146, 0.9044, 0.8937, 0.8824, 0.8706, 0.8583, 0.8454, 
    0.8321, 0.8182, 0.8039, 0.7890, 0.7737, 0.7580, 0.7417, 0.7251, 
    0.7080, 0.6904, 0.6725, 0.6541, 0.6354, 0.6162, 0.5967, 0.5769, 
    0.5566, 0.5361, 0.5152, 0.4941, 0.4726, 0.4508, 0.4288, 0.4065, 
    0.3840, 0.3612, 0.3382, 0.3150, 0.2917, 0.2681, 0.2444, 0.2205, 
    0.1966, 0.1724, 0.1482, 0.1239, 0.0996, 0.0751, 0.0506, 0.0261, 
    0.0016, -0.0229, -0.0475, -0.0719, -0.0964, -0.1208, -0.1451, -0.1693, 
    -0.1934, -0.2174, -0.2413, -0.2650, -0.2886, -0.3120, -0.3352, -0.3582, 
    -0.3810, -0.4036, -0.4259, -0.4480, -0.4698, -0.4913, -0.5125, -0.5334, 
    -0.5540, -0.5743, -0.5942, -0.6137, -0.6329, -0.6517, -0.6701, -0.6881, 
    -0.7057, -0.7229, -0.7396, -0.7559, -0.7717, -0.7871, -0.8020, -0.8164, 
    -0.8303, -0.8437, -0.8566, -0.8690, -0.8809, -0.8923, -0.9031, -0.9133, 
    -0.9230, -0.9322, -0.9408, -0.9488, -0.9563, -0.9632, -0.9695, -0.9752, 
    -0.9803, -0.9849, -0.9888, -0.9922, -0.9950, -0.9971, -0.9987, -0.9996, 
    -1.0000, -0.9998, -0.9989, -0.9975, -0.9954, -0.9928, -0.9895, -0.9857, 
    -0.9813, -0.9762, -0.9706, -0.9644, -0.9577, -0.9503, -0.9424, -0.9339, 
    -0.9249, -0.9153, -0.9051, -0.8944, -0.8832, -0.8714, -0.8591, -0.8463, 
    -0.8330, -0.8191, -0.8048, -0.7900, -0.7747, -0.7590, -0.7428, -0.7262, 
    -0.7091, -0.6916, -0.6736, -0.6553, -0.6366, -0.6175, -0.5980, -0.5782, 
    -0.5580, -0.5374, -0.5166, -0.4954, -0.4740, -0.4522, -0.4302, -0.4080, 
    -0.3854, -0.3627, -0.3397, -0.3166, -0.2932, -0.2696, -0.2459, -0.2221, 
    -0.1981, -0.1740, -0.1498, -0.1255, -0.1011, -0.0767, -0.0522, -0.0277
};

double sine(double x, double lut(TABLE_SIZE))
{
  bool negateTableValue = false;
  if (x < 0) {
    // sin(-x) = -sin(x)
    x = -x;
    negateTableValue = true;
  }
  
  uint8_t index_01 = x/STEP_SIZE;
  uint8_t index_02 = (index_01 + 1);
      
  double aux = (lut(index_02) - lut(index_01))/STEP_SIZE*(x - index_01*STEP_SIZE) + lut(index_01);
  
  if (negateTableValue) {
    return -aux;
  } else {
    return aux;
  } 
}

The sine values calculation is based on the look-up table containing the pre-computed values of the sine function covering the whole period $left<0, 2piright>$ with 256 values. I have decided to use the linear interpolation method for improving the precision.

I have one doubt regarding the linear interpolation. Namely I have been using table with 256
entries but most of the solutions exploiting the linear interpolation use look-up table with one additional entry. I would say that it isn’t necessary in my case because the index variables are uint8_t type i.e. they can store values from range 0-255. But I would like to know other ones opinion. Thank you in advance.