// Some externally defined stuff
//#define SCALE (sizeof(BASE) * 8)
//#define RADIX 16
//#define BASIS ((BASE)1 << RADIX)
//#define PI (BASE)(3.1415926536897932384626 * BASIS)
//typedef Sclr int64_t;
//typedef Angl int64_t;

Sclr
engineer_math_sin(Angl input)
{
   // A sine approximation via a fifth-order polynomial.
   int64_t c, x, x2, o;
   static const int64_t
      A  = PI/2,                        // PI/2
      B  = PI - (5 * BASIS)/2,          // PI - 5/2
      C  = (PI - 3 * BASIS)/2,          // (PI - 3)/2
      S  = (BASIS << (RADIX + 1)) / PI; // 2/PI

    x = MULT(input, S);

    x = x << (62 - RADIX);         // Shift to full s64 range (Q16->Q62)
    if( (x ^ (x << 1)) < 0)        // Test for quadrant 1 or 2
       x = ((int64_t)1 << 63) - x;
    x = x >> (62 - RADIX);

    x2 =     MULT(x, x);   // Ax - Bx^3 + Cx^5
    o  = B - MULT(C, x2);  // Ax - x(Bx^2 - Cx^4)
    o  = A - MULT(o, x2);  // x(A - (Bx^2 - Cx^4)
    o  =     MULT(o, x);   // x(A - x^2(B - Cx^2))

    return o;
}