; maximum difference in an array
(define (range . args)
(case (length args)
((1) (range 0 (car args) (if (negative? (car args)) -1 1)))
((2) (range (car args) (cadr args) (if (< (car args) (cadr args)) 1 -1)))
((3) (let ((le? (if (negative? (caddr args)) >= <=)))
(let loop ((x(car args)) (xs '()))
(if (le? (cadr args) x)
(reverse xs)
(loop (+ x (caddr args)) (cons x xs))))))
(else (error 'range "unrecognized arguments"))))
(define rand #f)
(define randint #f)
(let ((two31 #x80000000) (a (make-vector 56 -1)) (fptr #f))
(define (mod-diff x y) (modulo (- x y) two31)) ; generic version
; (define (mod-diff x y) (logand (- x y) #x7FFFFFFF)) ; fast version
(define (flip-cycle)
(do ((ii 1 (+ ii 1)) (jj 32 (+ jj 1))) ((< 55 jj))
(vector-set! a ii (mod-diff (vector-ref a ii) (vector-ref a jj))))
(do ((ii 25 (+ ii 1)) (jj 1 (+ jj 1))) ((< 55 ii))
(vector-set! a ii (mod-diff (vector-ref a ii) (vector-ref a jj))))
(set! fptr 54) (vector-ref a 55))
(define (init-rand seed)
(let* ((seed (mod-diff seed 0)) (prev seed) (next 1))
(vector-set! a 55 prev)
(do ((i 21 (modulo (+ i 21) 55))) ((zero? i))
(vector-set! a i next) (set! next (mod-diff prev next))
(set! seed (+ (quotient seed 2) (if (odd? seed) #x40000000 0)))
(set! next (mod-diff next seed)) (set! prev (vector-ref a i)))
(flip-cycle) (flip-cycle) (flip-cycle) (flip-cycle) (flip-cycle)))
(define (next-rand)
(if (negative? (vector-ref a fptr)) (flip-cycle)
(let ((next (vector-ref a fptr))) (set! fptr (- fptr 1)) next)))
(define (unif-rand m)
(let ((t (- two31 (modulo two31 m))))
(let loop ((r (next-rand)))
(if (<= t r) (loop (next-rand)) (modulo r m)))))
(init-rand 19380110) ; happy birthday donald e knuth
(set! rand (lambda seed
(cond ((null? seed) (/ (next-rand) two31))
((eq? (car seed) 'get) (cons fptr (vector->list a)))
((eq? (car seed) 'set) (set! fptr (caadr seed))
(set! a (list->vector (cdadr seed))))
(else (/ (init-rand (modulo (numerator
(inexact->exact (car seed))) two31)) two31)))))
(set! randint (lambda args
(cond ((null? (cdr args))
(if (< (car args) two31) (unif-rand (car args))
(floor (* (next-rand) (car args)))))
((< (car args) (cadr args))
(let ((span (- (cadr args) (car args))))
(+ (car args)
(if (< span two31) (unif-rand span)
(floor (* (next-rand) span))))))
(else (let ((span (- (car args) (cadr args))))
(- (car args)
(if (< span two31) (unif-rand span)
(floor (* (next-rand) span))))))))))
(define (shuffle x)
(do ((v (list->vector x)) (n (length x) (- n 1)))
((zero? n) (vector->list v))
(let* ((r (randint n)) (t (vector-ref v r)))
(vector-set! v r (vector-ref v (- n 1)))
(vector-set! v (- n 1) t))))
(define-syntax assert
(syntax-rules ()
((assert expr result)
(if (not (equal? expr result))
(for-each display `(
#\newline "failed assertion:" #\newline
expr #\newline "expected: " ,result
#\newline "returned: " ,expr #\newline))))))
(define (max-diff-quadratic xv)
(define (x n) (vector-ref xv n))
(let ((len (vector-length xv)))
(let ((lo 0) (hi 0) (diff 0))
(do ((i 0 (+ i 1))) ((= i len) (list lo hi diff))
(do ((j (+ i 1) (+ j 1))) ((= j len))
(let ((d (- (x j) (x i))))
(when (< diff d)
(set! lo i) (set! hi j) (set! diff d))))))))
(define (max-diff-linear xv)
(define (x n) (vector-ref xv n))
(let loop ((k 0) (lo 0) (hi 0) (min-lo 0) (max-d 0))
(if (= (vector-length xv) k)
(list lo hi max-d)
(let* ((min-lo (if (< (x k) (x min-lo)) k min-lo))
(d (- (x k) (x min-lo))))
(if (< max-d d)
(loop (+ k 1) min-lo k min-lo d)
(loop (+ k 1) lo hi min-lo max-d))))))
(define (max-diff-test)
(assert (max-diff-quadratic #(4 3 9 1 8 2 6 7 5)) '(3 4 7))
(assert (max-diff-quadratic #(4 2 9 1 8 3 6 7 5)) '(1 2 7))
(assert (max-diff-quadratic #(4 3 9 1 2 6 7 8 5)) '(3 7 7))
(assert (max-diff-quadratic #(5 4 3)) '(0 0 0))
(assert (max-diff-quadratic #(1 3 3)) '(0 1 2))
(assert (max-diff-linear #(4 3 9 1 8 2 6 7 5)) '(3 4 7))
(assert (max-diff-linear #(4 2 9 1 8 3 6 7 5)) '(1 2 7))
(assert (max-diff-linear #(4 3 9 1 2 6 7 8 5)) '(3 7 7))
(assert (max-diff-linear #(5 4 3)) '(0 0 0))
(assert (max-diff-linear #(1 3 3)) '(0 1 2))
(do ((i 0 (+ i 1))) ((= i 1000))
(let ((x (list->vector (shuffle (range 1 25)))))
(assert (max-diff-quadratic x) (max-diff-linear x))))
(do ((i 0 (+ i 1))) ((= i 25))
(let ((x (list->vector (shuffle (range 1 1000)))))
(assert (max-diff-quadratic x) (max-diff-linear x)))))
(max-diff-test)