Very accurate and fast sine computation based on Bhaskara I's sine approximation formula. https://en.wikipedia.org/wiki/Bhaskara_I%27s_sine_approximation_formula

fast_sin.c

#define E_PI    3.141592653589793238462643383279502884197169399375105820974
#define E_TAU   6.283185307179586476925286766559005768394338798750211641950
#define E_PI_SQ 9.869604401089358618834490999876151135313699407240790626413

double fast_sin(double var){
  int loops = var/(2*E_PI);
  var = var - loops*2*E_PI;

  if(var>E_PI){
    var = E_PI - var;
  }else if((-var)>E_PI){
    var = -E_PI - var;
  }// Make the angle to be between -pi and pi

  if(var<0){
    var = -var;
    return -(16.0*var*(E_PI - var))/(5.0*E_PI_SQ - 4.0*var*(E_PI - var)); // Sine is an odd function -> sin(x) = -sin(x)
  }else{
    return (16.0*var*(E_PI - var))/(5.0*E_PI_SQ - 4.0*var*(E_PI - var));
  }
}