sin.c

#define pi 3.1415926535897932

double sin(double a) {
  double y;

  double x = a / (pi / 2);
  int fol = x;
  int neg = (int)(x / 2) & 1;
  int inv = (int)x & 1;

  x = x - fol; // fold
  x = (1 - inv) * x + inv * (1 - x); // invert?
  a = x * (pi / 2);
  y = a * (1 - a*a/6 * (1 - a*a/20 * (1 - a*a/42 * (1 - a*a/72 *
    (1 - a*a/110 * (1 - a*a/156 * (1 - a*a/210 * (1 - a*a/272 *
    (1 - a*a/342 * (1 - a*a/420))))))))));

  y = neg * -y + (1 - neg) * y; // negate?

  return y;
}