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;; Copyright (c) Stephen C. Gilardi. All rights reserved.
;; The use and distribution terms for this software are covered by the
;; Common Public License 1.0 (http://opensource.org/licenses/cpl.php)
;; which can be found in the file CPL.TXT at the root of this distribution.
;; By using this software in any fashion, you are agreeing to be bound by
;; the terms of this license.
;; You must not remove this notice, or any other, from this software.
;;
;; lazy-seqs.clj
;;
;; Lazy sequences
;;
;; primes - based on the "naive" implemention described in [1] plus a
;; small "wheel" which eliminates multiples of 2, 3, 5, and
;; 7 from consideration by incrementing past them. Also inspired
;; by code from Christophe Grand in [2].
;;
;; fibs - based on code from Rich Hickey at the Clojure wiki [3]
;;
;; [1] http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf
;; [2] http://clj-me.blogspot.com/2008/06/primes.html
;; [3] http://en.wikibooks.org/wiki/Clojure_Programming#Examples
;;
;; scgilardi (gmail)
;; 07 June 2008
(clojure/in-ns 'lazy-seqs)
(clojure/refer 'clojure)
(lib/use def)
(defvar primes
(lazy-cat [2 3 5 7]
(let [primes-from
(fn primes-from [n [f & r]]
(if (some #(zero? (rem n %)) (take-while #(<= (* % %) n) primes))
(recur (+ n f) r)
(lazy-cons n (primes-from (+ n f) r))))
wheel (cycle [2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2
6 4 6 8 4 2 4 2 4 8 6 4 6 2 4 6
2 6 6 4 2 4 6 2 6 4 2 4 2 10 2 10])]
(primes-from 11 wheel)))
"A lazy sequence of all the prime numbers.")
(defvar fibs
(concat [0 1]
(let [rest-fn
(fn rest-fn [a b]
(let [next (+ a b)]
(lazy-cons next (rest-fn b next))))]
(rest-fn 0 1)))
"A lazy sequence of all the fibonacci numbers.")
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