/// <summary>
/// Mandelbrot calculations, optimized.
/// Gains a speed factor 3.1 compared to a lazy 'c# with GMP Real' implementation.
///
/// Calculates:
/// tmp = 2*x*y + y0
/// x = x*x - y*y + x0
/// y = tmp
///
/// Remarks: All Parameters must be properly created.
///
/// Example implementation, calculates one pixel:
///
/// int iterations = 0;
/// Real x0 = new Real(your x coordinate);
/// Real y0 = new Real(your y coordinate);
/// Real x = new Real(x0);
/// Real y = new Real(y0);
/// Real temp = new Real();
///
/// while ((iterations < maxIterations) && (x.DoubleValue * x.DoubleValue + y.DoubleValue * y.DoubleValue <= 4))
/// {
/// Real.MandelbrotOperations(ref x, ref y, ref x0, ref y0, ref temp);
/// iteration++;
/// }
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="x0"></param>
/// <param name="y0"></param>
public static void MandelbrotOperations(ref Real x, ref Real y, ref Real x0, ref Real y0, ref Real tmp)
{
// t = 2*x*y+y0
mpf_mul(ref tmp._pointer, ref x._pointer, ref y._pointer);
mpf_mul_ui(ref tmp._pointer, ref tmp._pointer, (uint)2);
mpf_add(ref tmp._pointer, ref tmp._pointer, ref y0._pointer);
// x = x*x - y*y + x0
mpf_mul(ref y._pointer, ref y._pointer, ref y._pointer); // y = y*y
mpf_mul(ref x._pointer, ref x._pointer, ref x._pointer); // x = x*x
mpf_sub(ref x._pointer, ref x._pointer, ref y._pointer); // x = x-y
mpf_add(ref x._pointer, ref x._pointer, ref x0._pointer); // x = x+x0
// exchange y and t the FAST way :)
mpf_t temp_mpf_t = y._pointer;
y._pointer = tmp._pointer;
tmp._pointer = temp_mpf_t;
}
private static extern void mpf_init(ref mpf_t ptr);
private static extern void mpf_neg(ref mpf_t rop, ref mpf_t op);
private static extern void mpf_sqrt_ui(ref mpf_t rop, uint op);
private static extern int mpf_integer_p(ref mpf_t op);
private static extern int mpf_floor(ref mpf_t rop, ref mpf_t op);
private static extern int mpf_cmp_ui(ref mpf_t op1, uint op2);
private static extern int mpf_cmp_d(ref mpf_t op1, double op2);
private static extern void mpf_init_set(ref mpf_t rop, ref mpf_t op);
private static extern int mpf_swap(ref mpf_t rop1, ref mpf_t rop2);
private static extern void mpf_set_z(ref mpf_t rop, ref mpz_t op);
private static extern void mpf_set_prec(ref mpf_t ptr, uint prec);
private static extern uint mpf_get_prec(ref mpf_t ptr);
private static extern void mpf_clear(ref mpf_t ptr);
private static extern void mpf_init2(ref mpf_t ptr, uint prec);
private static extern void mpf_ui_div(ref mpf_t rop, uint op1, ref mpf_t op2);
private static extern int mpf_cmp(ref mpf_t op1, ref mpf_t op2);
private static extern void mpf_init_set_si(ref mpf_t rop, int op);
private static extern int mpf_cmp_si(ref mpf_t op1, int op2);
private static extern void mpf_init_set_d(ref mpf_t rop, double op);
private static extern void mpf_ceil(ref mpf_t rop, ref mpf_t op);
private static extern int mpf_init_set_str(ref mpf_t rop, IntPtr s, int sbase);
private static extern int mpf_trunc(ref mpf_t rop, ref mpf_t op);
private static extern double mpf_get_d(ref mpf_t op);
private static extern void mpf_sqrt(ref mpf_t rop, ref mpf_t op);
private static extern int mpf_get_si(ref mpf_t op);
private static extern void mpf_pow_ui(ref mpf_t rop, ref mpf_t op1, uint op2);
private static extern IntPtr mpf_get_str(IntPtr s, ref int expptr, int sbase, int ndigits, ref mpf_t op);
private static extern void mpq_set_f(ref mpq_t rop, ref mpf_t op);
private static extern void mpf_mul(ref mpf_t rop, ref mpf_t op1, ref mpf_t op2);
