RGB->HSI->RGB

Hello

I'm having quantisation problems swapping between different colour spaces in
a reversible way and wondered if anyone had a solution or a suggestion to
the problem.

At present I'm using fp arithmetic to convert 3 byte rgb to 3 byte hsi.
Unfortunately the reverse of this procedure does not give exactly the same
rgb and after a few loops around this process there is a significant shift.

I suppose one solution would be to use some form of look-up table and its
inverse, but the number of permutations seems too large for that.

Any ideas?

Thanks
Pete