Efficient Implemention of Lagrange Quadratic Interpolation?

Hi,

So basically, my understanding of lagrange quadratic is this

a(T) = L0( T )a( T0 ) + L1(T)a(T1) + L2(T)a(T2)

with L0(T) = ( (T - T1)/(T0 - T1) )( (T - T2)/(T0 - T2))
etc with L1(T) and L2(T)

On paper, a few addition, multiplication, and even a division. Isn't hard at all.

However, I'm doing this on a DSP, so no division. The target is 8X interpolation in time domain. My input is random complex number represented by a real array and an complex array(int16).

What is confusing me is this: I have a report on the same interpolation implemented on the same DSP(same random complex input, 8x). It mentions that the "interpolation coefficients" are generated by a seperated C program and is hard coded in the memory.

What exactly are these magical fixed coefficients? To me, it looks like L0(T), L1(T), and L2(T) need to be recompute for every sample. The coefficients seem to be refering to some kind of filtering technique in work here. Am I missing something?

Thanks