#lang pl

; I'm keeping my own type declarations bc the racket ones are literally unreadable.
; gcd2: a: Int, b: Int → Int
(: gcd2 : (Integer Integer -> Integer))
; Given two non-negative integers, determine their greatest common divisor.
(define (gcd2 a b)
  (cond
    [(or (negative? a) (negative? b)) (error 'neg "Given negative number.")]
    [(= a 0) b]
    [(= b 0) a]
    [(and (even? a) (even? b)) (* 2 (gcd2 (floor (/ a 2)) (floor (/ b 2))))]
    [(even? b) (gcd2 a (floor (/ b 2)))]
    [(even? a) (gcd2 (floor (/ a 2)) b)]
    [else
     (if (<= a b)
         (gcd2 a (- b a))
         (gcd2 b (- a b)))]))

(test (gcd2 0 0) => 0)
(test (gcd2 288 64) => 32)
; What's the point of the symbol in the error definition if it isn't used to check errors?
(test (gcd2 2 -1) =error> "Given negative number.")

; out-of-bounds?: start: Number,
;                 lower: Number,
;                 upper: Number, 
;                 l: [Number] → Bool
(: out-of-bounds? : (Number Number Number (Listof Number) -> Boolean))
; Determines if an object that begins at the starting location and then moves delta by delta ever ever steps outside of the bounds (inclusive).
(define (out-of-bounds? start lower upper l)
  (if (or (< start lower) (> start upper))
      #t
      (match l
        ['() #f]
        [(cons frst rst) (out-of-bounds? frst lower upper rst)])))

(test (out-of-bounds? 0 -1 2 '(0 -2 3 -4 6)) => #t)
(test (out-of-bounds? 0 -1 1 '(1)) => #f)
(test (out-of-bounds? 0 -1 1 '()) => #f)
(test (out-of-bounds? 0 1 2 '()) => #t)
(test (out-of-bounds? 0 0 0 '()) => #f)