In a function call, the state (the current computation being done) is saved anyway, and therefore "copied" if that is your preferred term. So ideally, call/cc should have the same overhead as an ordinary function call; the only difference is that in call/cc the continuation state is the value given to the function, while in a function call it's just one of the values given to the function.
Note however that much of the theoretical analyses of call/cc make a basic assumption of a "spaghetti stack", which would mean that partially unwound stacks would be saved implicitly as long as any continuation exists which refers to that stack, and all stacks themselves are subject to garbage collection. Most machines don't actually have a spaghetti stack and can't make a spaghetti stack anyway ^^. That said a spaghetti stack could be implemented as a simple list, with push == cons and pop = cdr.
Alternatively store the local variables on a garbage-collected heap, and include a reference to the local variables with the continuation/return address (you'll probably need to save the pointer-to-local-variables anyway, since the target function is likely to use that pointer for its own locals). Again, no additional overhead over plain function calls, except perhaps to restructure the return address and the pointer-to-local-variables.
Don't know about MIT Scheme, but if I were to implement call/cc on stock hardware and compiling down to machine language that's what I'd do ^^
I'm still totally not understanding your claim that call/cc should have the same overhead as an ordinary function call.
I read the Clinger "Implementation Strategies for Continuations" paper and they found call/cc about 10 times slower than function calls on the tak/ctak tests. I tried those tests on PLT Scheme and the overhead I saw is even worse: .7 seconds with function calls vs 51.8 seconds with continuations on (tak 24 16 8).
Clinger says about the stack strategy: "When a continuation is captured, however, a copy of the entire stack is made and stored in the heap. ... Variations on the stack strategy are used by most implementations of Scheme and Smalltalk-80."
Components of function call: (1) put arguments somewhere (2) put return address somewhere (3) jump to function.
Components of call/cc: (1) put return address as argument somewhere (2) put return address somewhere (3) jump to function.
That said, continuations generally assume that "put X somewhere" means somewhere != stack. Yes, even return addresses are not intended to be on the stack when using continuations. The main problem is when compiling down to C, which always assumes that somewhere == stack. If you're compiling down to machine language where you have access to everything, then you can just ignore the stack, but not in C, which inherently expects the stack.
