Why was a stack-based C API chosen?

["Joseph C. Sible" <josephcsible@...>]

A lot of emphasis is placed on the fact that Lua bytecode runs on a
register-based VM, rather than on a stack-based VM, and that this is
significant for performance reasons. Why is the Lua C API then
stack-based instead of also being register-based for the same reason?

Joseph C. Sible