There were discussion even earlier in this group on this.
Kalingathu Parani, hails each chola kings who were predecessors, to Abaya Kulothunga. For Karikalan the line starts with 'Karai sEi Ponniyil...'. So, this proves, that it as built by a King, who lived long ago, even before, Nayakar's great grand fathers were born.
It is a part of Srilanka, history that Karikalan, brougt PoW from his Srilanka war, to have this constructed. It is a different story that there was a revenge from Srilanka side too.
-kallanai a natural dam? no way I quote what i have read it is thought to date back to the 1st or 2nd century. It is considered the oldest water-diversion structure in the world still in use. an older dam in egypt recently covered in discovery channel is not inoperation The Kallanai is a massive dam of unhewn stone, 329 metres (1,080 feet) long and 20 metres (60 feet) wide, across the main stream of the Cauvery. figures may vary but definitely man made.perhaps he used a natural cataract for the site.