; array duplicates
(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 (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 (vector-sort! vec comp)
(define-syntax while
(syntax-rules ()
((while pred? body ...)
(do () ((not pred?)) body ...))))
(define-syntax assign!
(syntax-rules ()
((assign! var expr)
(begin (set! var expr) var))))
(define len (vector-length vec))
(define-syntax v (syntax-rules () ((v k) (vector-ref vec k))))
(define-syntax v! (syntax-rules () ((v! k x) (vector-set! vec k x))))
(define-syntax cmp (syntax-rules () ((cmp a b) (comp (v a) (v b)))))
(define-syntax lt? (syntax-rules () ((lt? a b) (negative? (cmp a b)))))
(define-syntax swap! (syntax-rules () ((swap! a b)
(let ((t (v a))) (v! a (v b)) (v! b t)))))
(define (vecswap! a b s)
(do ((a a (+ a 1)) (b b (+ b 1)) (s s (- s 1))) ((zero? s))
(swap! a b)))
(define (med3 a b c)
(if (lt? b c)
(if (lt? b a) (if (lt? c a) c a) b)
(if (lt? c a) (if (lt? b a) b a) c)))
(define (pv-init a n)
(let ((pm (+ a (quotient n 2))))
(when (> n 7)
(let ((pl a) (pn (+ a n -1)))
(when (> n 40)
(let ((s (quotient n 8)))
(set! pl (med3 pl (+ pl s) (+ pl s s)))
(set! pm (med3 (- pm s) pm (+ pm s)))
(set! pn (med3 (- pn s s) (- pn s) pn))))
(set! pm (med3 pl pm pn))))
pm))
(let qsort ((a 0) (n len))
(if (< n 7)
(do ((pm (+ a 1) (+ pm 1))) ((not (< pm (+ a n))))
(do ((pl pm (- pl 1)))
((not (and (> pl a) (> (cmp (- pl 1) pl) 0))))
(swap! pl (- pl 1))))
(let ((pv (pv-init a n)) (r #f)
(pa a) (pb a) (pc (+ a n -1)) (pd (+ a n -1)))
(swap! a pv) (set! pv a)
(let loop ()
(while (and (<= pb pc) (<= (assign! r (cmp pb pv)) 0))
(when (= r 0) (swap! pa pb) (set! pa (+ pa 1)))
(set! pb (+ pb 1)))
(while (and (>= pc pb) (>= (assign! r (cmp pc pv)) 0))
(when (= r 0) (swap! pc pd) (set! pd (- pd 1)))
(set! pc (- pc 1)))
(unless (> pb pc)
(swap! pb pc) (set! pb (+ pb 1)) (set! pc (- pc 1)) (loop)))
(let ((pn (+ a n)))
(let ((s (min (- pa a) (- pb pa)))) (vecswap! a (- pb s) s))
(let ((s (min (- pd pc) (- pn pd 1)))) (vecswap! pb (- pn s) s))
(let ((s (- pb pa))) (when (> s 1) (qsort a s)))
(let ((s (- pd pc))) (when (> s 1) (qsort (- pn s) s))))))))
(define (sorting vec)
(define (cmp lt?) (lambda (a b) (if (lt? a b) -1 (if (lt? b a) 1 0))))
(vector-sort! vec (cmp <))
(do ((i 1 (+ i 1)))
((= (vector-ref vec i) (vector-ref vec (- i 1)))
(vector-ref vec i))))
(define (searching vec)
(let ((bits (make-vector (vector-length vec) #f)))
(do ((i 0 (+ i 1)))
((vector-ref bits (vector-ref vec i))
(vector-ref vec i))
(vector-set! bits (vector-ref vec i) #t))))
(define (gaussian vec)
(let ((n (vector-length vec)))
(do ((i 0 (+ i 1))
(sum 0 (+ sum (vector-ref vec i))))
((= i n) (- sum (* (- n 1) n 1/2))))))
(define x (apply vector (shuffle (cons 1776 (range 1 100001)))))
(time (display (gaussian x))) (newline)
(time (display (searching x))) (newline)
(time (display (sorting x))) (newline)