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 ;; Copyright (c) Stephen C. Gilardi. All rights reserved. The use and ;; distribution terms for this software are covered by the Eclipse Public ;; License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) which can ;; be found in the file epl-v10.html 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 ;; ;; == 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 - all the Fibonacci numbers ;; ;; powers-of-2 - all the powers of 2 ;; ;; == Lazy sequence functions == ;; ;; (partition-all, shuffle moved to clojure.core) ;; (rand-elt moved to clojure.core/rand-nth) ;; (rotations, moved to seq_utils.clj) ;; (permutations and combinations moved to combinatorics.clj) ;; ;; [1] http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf ;; [2] http://clj-me.blogspot.com/2008/06/primes.html ;; ;; scgilardi (gmail) ;; Created 07 June 2008 (ns ^{:author "Stephen C. Gilardi", :doc " ==== 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 - all the Fibonacci numbers powers-of-2 - all the powers of 2 ==== Lazy sequence functions ==== (partition-all, shuffle moved to clojure.core) (rand-elt moved to clojure.core/rand-nth) (rotations, rand-elt moved to seq_utils.clj) (permutations and combinations moved to combinatorics.clj) [1] http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf [2] http://clj-me.blogspot.com/2008/06/primes.html "} clojure.contrib.lazy-seqs (:use clojure.contrib.def)) ; primes cannot be written efficiently as a function, because ; it needs to look back on the whole sequence. contrast with ; fibs and powers-of-2 which only need a fixed buffer of 1 or 2 ; previous values. (defvar primes (concat [2 3 5 7] (lazy-seq (let [primes-from (fn primes-from [n [f & r]] (if (some #(zero? (rem n %)) (take-while #(<= (* % %) n) primes)) (recur (+ n f) r) (lazy-seq (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)))) "Lazy sequence of all the prime numbers.") (defn fibs "Returns a lazy sequence of all the Fibonacci numbers." [] (map first (iterate (fn [[a b]] [b (+ a b)]) [0 1]))) (defn powers-of-2 "Returns a lazy sequence of all the powers of 2" [] (iterate #(bit-shift-left % 1) 1))
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