Design and write recursive functions over the natural numbers.
Write a recursive procedure, (bounded-power-of-2 n), that finds the largest integer power of 2 less than of equal to the positive integer n.
(check-equal? (bounded-power-of-2 1)
1
"edge case/base case: 2^0")
(check-equal? (bounded-power-of-2 2)
2
"edge case/base case: 2^1")
(check-equal? (bounded-power-of-2 3)
2
"normal case: small non-power-of-two")
(check-equal? (bounded-power-of-2 7)
4
"normal case: small non-power-of-two")
(check-equal? (bounded-power-of-2 16)
16
"normal case: relatively small power of 2")
(check-equal? (bounded-power-of-2 17)
16
"normal case: relatively small non-power-of-two")
(check-equal? (bounded-power-of-2 72)
64
"normal case: somewhat larger non-powr-of-two")
(check-equal? (bounded-power-of-2 (expt 2 123))
(expt 2 123)
"edge case: large power of 2")
(check-equal? (bounded-power-of-2 (+ (expt 2 123) 123))
(expt 2 123)
"edge case: large non-power of 2")