; shellsort with three increments
(define (isqrt n)
(if (not (and (positive? n) (integer? n)))
(error 'isqrt "must be positive integer")
(let loop ((x n))
(let ((y (quotient (+ x (quotient n x)) 2)))
(if (< y x) (loop y) x)))))
(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 (shellsort lt? vec gaps)
(let ((n (vector-length vec)))
(do ((gaps gaps (cdr gaps))) ((null? gaps) vec)
(let ((g (car gaps)))
(do ((i g (+ i 1))) ((<= n i))
(let ((t (vector-ref vec i)))
(do ((j i (- j g)))
((or (< j g)
(<= (vector-ref vec (- j g)) t))
(vector-set! vec j t))
(vector-set! vec j
(vector-ref vec (- j g))))))))))
(define (gaps n)
(define (coprime? x y) (= (gcd x y) 1))
(let* ((h (isqrt n)) (g (isqrt h)))
(let loop ((g g))
(if (coprime? h g)
(list h g 1)
(loop (- g 1))))))
(define (rand-vector n)
(let ((vec (make-vector n)))
(do ((i 0 (+ i 1))) ((= i n) vec)
(vector-set! vec i (randint 1000000)))))
(display (shellsort < (rand-vector 50) (gaps 50)))