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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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