[ create a new paste ] login | about

Project: programmingpraxis
Link: http://programmingpraxis.codepad.org/O6J0rkDn    [ raw code | output | fork ]

programmingpraxis - Scheme, pasted on Oct 3:
; sieve of sundaram

(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"))))

; eratosthenes

(define (primes n)
  (let* ((max-index (quotient (- n 3) 2))
         (v (make-vector (+ 1 max-index) #t)))
    (let loop ((i 0) (ps '(2)))
      (let ((p (+ i i 3)) (startj (+ (* 2 i i) (* 6 i) 3)))
        (cond ((>= (* p p) n)
               (let loop ((j i) (ps ps))
                  (cond ((> j max-index) (reverse ps))
                        ((vector-ref v j)
                          (loop (+ j 1) (cons (+ j j 3) ps)))
                        (else (loop (+ j 1) ps)))))
              ((vector-ref v i)
                (let loop ((j startj))
                  (if (<= j max-index)
                      (begin (vector-set! v j #f)
                             (loop (+ j p)))))
                      (loop (+ 1 i) (cons p ps)))
              (else (loop (+ 1 i) ps)))))))

(display "Eratosthenes: ") (time (display (length (primes 2000000))) (display " "))

; segmented

(define (primes . args) ; (primes [lo] hi) inclusive at both ends
  (let* ((lo (if (null? (cdr args)) 0 (car args)))
         (hi (if (null? (cdr args)) (car args) (cadr args))))
    (cond ((and (<= lo 100000) (<= hi 1000000)) ; simple sieve
           (let* ((max-index (quotient (- hi 3) 2))
                  (v (make-vector (+ max-index 1) #t)))
             (let loop ((i 0) (ps (list 2)))
               (let ((p (+ i i 3)) (startj (+ (* 2 i i) (* 6 i) 3)))
                 (cond ((< hi (* p p))
                        (let loop ((j i) (ps ps))
                          (cond ((< max-index j)
                                 (let loop ((ps (reverse ps)))
                                   (if (<= lo (car ps)) ps
                                     (loop (cdr ps)))))
                                ((vector-ref v j)
                                 (loop (+ j 1) (cons (+ j j 3) ps)))
                                (else (loop (+ j 1) ps)))))
                       ((vector-ref v i)
                        (let loop ((j startj))
                          (when (<= j max-index)
                            (vector-set! v j #f) (loop (+ j p))))
                        (loop (+ i 1) (cons p ps)))
                       (else (loop (+ i 1) ps)))))))
          ((< lo (sqrt hi))
           (let* ((r (inexact->exact (ceiling (sqrt hi))))
                  (r (if (even? r) r (+ r 1))))
             (append (primes lo r) (primes r hi))))
          (else ; segmented sieve
           (let* ((lo (if (even? lo) lo (- lo 1)))
                  (b 50000) (bs (make-vector b #t))
                  (r (inexact->exact (ceiling (sqrt hi))))
                  (ps (cdr (primes r)))
                  (qs (map (lambda (p)
                             (modulo (* -1/2 (+ lo 1 p)) p)) ps))
                  (zs (list)) (z (lambda (p) (set! zs (cons p zs)))))
             (do ((t lo (+ t b b))
                  (qs qs (map (lambda (p q) (modulo (- q b) p))
                              ps qs)))
                 ((<= hi t)
                   (let loop ((zs zs))
                     (if (<= (car zs) hi) (reverse zs)
                       (loop (cdr zs)))))
               (do ((i 0 (+ i 1))) ((= i b)) (vector-set! bs i #t))
               (do ((ps ps (cdr ps)) (qs qs (cdr qs))) ((null? qs))
                 (do ((j (car qs) (+ j (car ps)))) ((<= b j))
                   (vector-set! bs j #f)))
               (do ((j 0 (+ j 1))) ((= j b))
                 (if (vector-ref bs j) (z (+ t j j 1))))))))))

(display "Segmented:    ") (time (display (length (primes 2000000))) (display " "))

; atkin

(define (primes limit)
  (define (exact x) (inexact->exact (floor x)))
  (let ((sieve (make-vector (+ (quotient limit 2) (modulo limit 2)) #f))
        (primes (list 3 2)))
    (define (flip! m) (vector-set! sieve m (not (vector-ref sieve m))))

    (let ((x-max (exact (sqrt (/ (- limit 1) 4)))) (x2 0))
      (do ((xd 4 (+ xd 8))) ((<= (+ (* x-max 8) 2) xd))
        (set! x2 (+ x2 xd))
        (let* ((y-max (exact (sqrt (- limit x2))))
               (n (+ x2 (* y-max y-max)))
               (n-diff (+ y-max y-max -1)))
          (when (even? n) (set! n (- n n-diff)) (set! n-diff (- n-diff 2)))
          (do ((d (* (- n-diff 1) 2) (- d 8))) ((<= d -1))
            (when (member (modulo n 12) (list 1 5)) (flip! (quotient n 2)))
            (set! n (- n d))))))

    (let ((x-max (exact (sqrt (/ (- limit 1) 3)))) (x2 0))
      (do ((xd 3 (+ xd 6))) ((<= (+ (* x-max 6) 2) xd))
        (set! x2 (+ x2 xd))
        (let* ((y-max (exact (sqrt (- limit x2))))
               (n (+ x2 (* y-max y-max)))
               (n-diff (+ y-max y-max -1)))
          (when (even? n) (set! n (- n n-diff)) (set! n-diff (- n-diff 2)))
          (do ((d (* (- n-diff 1) 2) (- d 8))) ((<= d -1))
            (when (= (modulo n 12) 7) (flip! (quotient n 2)))
            (set! n (- n d))))))

    (let ((x-max (exact (/ (+ (sqrt (- 4 (* (- 1 limit) 8))) 2) 4)))
          (y-min -1) (x2 0) (xd 3))
      (do ((x 1 (+ x 1))) ((<= (+ x-max 1) x))
        (set! x2 (+ x2 xd)) (set! xd (+ xd 6))
        (when (<= limit x2)
          (set! y-min (* (- (* (- (inexact->exact (ceiling (sqrt (- x2 limit)))) 1) 2) 2) 2)))
        (let ((n (- (* (+ (* x x) x) 2) 1))
              (n-diff (* (- (* (- x 1) 2) 2) 2)))
          (do ((d n-diff (- d 8))) ((<= d y-min))
            (when (= (modulo n 12) 11) (flip! (quotient n 2)))
            (set! n (+ n d))))))

    (do ((n 2 (+ n 1))) ((<= (quotient (+ (exact (sqrt limit)) 1) 2) n))
      (when (vector-ref sieve n)
        (let* ((p (+ n n 1)) (p2 (* p p)))
          (set! primes (cons p primes))
          (do ((k p2 (+ k (+ p2 p2)))) ((<= limit k))
            (vector-set! sieve (quotient k 2) #f)))))

    (do ((p (+ (exact (sqrt limit)) 1) (+ p 2))) ((<= limit p))
      (when (vector-ref sieve (quotient p 2))
        (set! primes (cons p primes))))

    (reverse primes)))

(display "Atkin:        ") (time (display (length (primes 2000000))) (display " "))

; sundaram

(define (primes n)
  (let* ((m (quotient n 2)) (pv (make-vector (+ m 1) #t)))
    (do ((i 1 (+ i 1))) ((< (quotient m 4) i))
      (do ((j i (+ j 1))) ((< (quotient (- m i) (+ i i 1)) j))
        (vector-set! pv (+ i j (* 2 i j)) #f)))
    (let loop ((i 1) (ps (list 2)))
      (cond ((= i m) (reverse ps))
            ((vector-ref pv i) (loop (+ i 1) (cons (+ i i 1) ps)))
            (else (loop (+ i 1) ps))))))

(display "Sundaram:     ") (time (display (length (primes 2000000))) (display " "))

; euler

(define (minus xs ys)
  (let loop ((xs xs) (ys ys) (zs '()))
    (cond ((null? ys) (append (reverse zs) xs))
          ((equal? (car xs) (car ys))
            (loop (cdr xs) (cdr ys) zs))
          (else (loop (cdr xs) ys (cons (car xs) zs))))))

(define (sub-list n p xs)
  (let loop ((xs xs) (zs '()))
    (let ((px (* p (car xs))))
      (if (< n px) (reverse zs)
        (loop (cdr xs) (cons px zs))))))

(define (euler n)
    (let loop ((xs (range 3 n 2)) (ps '(2)))
      (let ((p (car xs)))
        (if (< n (* p p))
            (append (reverse ps) xs)
            (loop (minus (cdr xs) (sub-list n p xs))
                  (cons p ps))))))

(display "Euler:        ") (time (display (length (primes 2000000))) (display " "))


Output:
1
2
3
4
5
Eratosthenes: 148933 cpu time: 100 real time: 738 gc time: 0
Segmented:    148933 cpu time: 140 real time: 791 gc time: 0
Atkin:        148933 cpu time: 180 real time: 953 gc time: 0
Sundaram:     148933 cpu time: 380 real time: 2317 gc time: 0
Euler:        148933 cpu time: 410 real time: 2123 gc time: 0


Create a new paste based on this one


Comments: