Function Description
********************

	Name: XY2 
	Function: Chemical Shift X+Y <-> XY + Y <+> XY2
	Parameters: S_LM1, Kd1, S_LM2, Kd2 

Notes
*****

	This function expects 3 column data.

	Use to fit chemical shift or linebroadening for binding equilibrium
	such as 
		P + L <-> P:L + L <-> P:L2
	when observing P and varying L. 

		Kd1 = [P][L]/[PL] 
		Kd2 = [PL][L]/[PL2]
		S_LM1 = dPL - dFree 
		S_LM2 = dPL2 - dFree

	Try holding Kd2 constant to achieve convergence.

Reference
*********

	141. Williams, T.C., J.G. Shelling and B.D. Sykes. NMR approaches to
	the characterization of the interaction of metal ions with proteins.
	In: NMR in the Life Sciences (Ed. E.M. Bradbury and C. Nicolini)
	Plenum Publishing Co., New York-London NATO-ASI Series A Life
	Sciences 107:93-103 (1986).

C-code for the function
***********************

	b = Kd2 - 4 * Kd1;
	c = Kd2 * Kd2;
	d = (c - (4 * Kd1 * Kd2) - (2 * x2 * Kd2)) / b;
	e = ((x * Kd2 * (2*x2 - x)) - (c * (x2 + Kd1 + x))) / b;
	f = -(2*d*d*d - 9*d*e + (27 * ((x*x2*c) / b))) / 54.0;
	g = (3*e - d*d) / 3.0;
	if (g > 0) return(FALSE);
	w = f / sqrt(-(g*g*g) / 27.0);
	if ((w > 1.0) || (w < -1.0)) return(FALSE);
	h = TO_DEG * acos(w);
	x3 = (2 * sqrt(-g/3.0) * cos(((h/3.0)+240)*TO_RAD) - (d/3.0));
	answer = ((S_LM1*x3) + (S_LM2*x3 * (x-x3)/(2*x3+Kd2))) / x2;