(*

power 2 3 = 8
power 3 2 = 9
power x 0 = 1

*)

let rec power x n =
  if n=0 
  then 1
  else x * (power x (n-1))

let power17 x = power x 17;;

let rec power' x n =
  if n=0 
  then .< 1 >.
  else .< .~x * .~(power' x (n-1)) >.

let codepower17 = .< fun z -> .~ (power' .<z>. 17) >.

let power17' = .! codepower17

(* power17' is about 4-5 times faster than power 17 in the
   MetaOCaml bytecode compiler *)

(* Q: How much time does it take to call power' and to compile? *)

let sqr x = x * x;;

let rec power x n =
  if n=0 
  then 1
  else 
    if (n mod 2) = 0
    then sqr (power x (n / 2))
    else x * (power x (n-1))

let power17 x = power x 17

let rec power' x n =
  if n=0 
  then .< 1 >.
  else 
    if (n mod 2) = 0
    then .< sqr .~(power' x (n / 2)) >.
    else .< .~x * .~(power' x (n-1)) >.

let codepower17' = .< fun z -> .~(power' .<z>. 17) >.

let power17' = .! codepower17'

(* Timing shows that staged power17' is still about 3 times faster than
   power17 (on 2), and it also looks like power17 is now 30% faster than
   before *)

(* Q: Can we produce code that just multiplies and doesn't need to
   call sqr? *)