;; qsort-library.ss and vector-library.ss (combined for hw9 convenience)
;;
;; export:
;;
;;   fori= : (num num num (num -> void) -> void)
;;   (* perform some action for some range of numbers *)
;;
;;   V* : ((vector num) (vector num) -> num)
;;
;; hidden: 
;;   reduce-vector : ((vector X) Y (X num Y -> Y) -> Y)
;;   (* vector-reduce *)

(unit/sig (fori= V* reduce-vector)
  (import plt:userspace^)

  (define (fori= start end step p)
    (if (>= start end) (void) 
      (begin (p start) (fori= (+ start step) end step p))))

;; reduce-vector:
;;   (num alpha (num (union alpha beta) -> beta) -> (union alpha beta))
;; N: num
;; base: alpha
;; combine: num (union alpha beta) -> beta
;; result: (union alpha beta)
;; Reduce the vector from right to left, structurally
(define (reduce-vector N base combine)
  (cond
    ((= N 0) base)
    (else (combine (sub1 N) (reduce-vector (sub1 N) base combine)))))

;; From vectors to lists
(define (vec->list vec)
  (reverse! 
    (reduce-vector (vector-length vec) null
      (lambda (i rest) (cons (vector-ref vec i) rest)))))

;(printf "test vec->list: ~s should be ~s~n"
;  (vec->list (vector 3 4)) (vector->list (vector 3 4)))

;; The norm of a vector
(define (norm vec)
  (sqrt (reduce-vector (vector-length vec) 0
	  (lambda (i rest) (+ (square (vector-ref vec i)) rest)))))
		  
(define (square x) (* x x))

;(printf "test norm: ~s should be 5~n" (norm (vector 3 4)))

;; The V* product of a vector
(define (V* vec1 vec2)
  (unless (= (vector-length vec1) (vector-length vec2))
    (error 'S* "the vectors must be of the same length"))
  (reduce-vector (vector-length vec1) 0
    (lambda (i rest) (+ (* (vector-ref vec1 i) (vector-ref vec2 i)) rest))))

;(printf "test s*: ~s should be 12~n" (s* (vector 3 4 5) (vector 1 1 1)))

  )