I'll cut to the chase--this is an absolutely impossible question to answer. Coming up with GDP figures today is not ready, coming up with them for places like Song China, for which we have enormous amounts of documentation and data, is very difficult and figures vary wildly. Coming up with figures for, say, the Chola, where this data does not exist, is impossible. Furthermore, thinking of these economies as unified, of a single "Chola economy" rather than multiple Chola economies, is a mistake. Even the Song had an economy that, by modern standards, was hopelessly poorly integrated. This is all leaving aside the question of what you measure this GDP in--modern analysis works because there are universal commodities, which is very much not the case.

Now, to go back a bit, the answer is very clearly Song China, which controlled an amount of land, population, and quality of production far above anyone else at the time. We can only say this, however, because there is such a massive gap. Determining a second place is simply not possible. And, again, this really only tells us about how we view the economy. We learn nothing about the Song, Chola, or Fatamids from such exercises.

And a follow up, was there maybe another fast(est) growing economy which was about to outgrow the Song Dynasty , byzantines economies, etc?

This not the perfect answer to your question but economies of the past were simpler, had much lower growth rates, and their respective sizes are more a function of the size of the population than they are today. With that in mind, the list would probably be something on the order of:

1: Song China

2: Chalyuka Dynasty (India)

3: Byzantine Empire

But these is just really an educated guess. Also in the mix could be the Buyids, the Chola Empire (south India) or the Fatamids (Syria, and all of North Africa up to Tunisia).