From 98b01afa04cd04796100b217b04f5f5f1b58e63e Mon Sep 17 00:00:00 2001
From: Colin Okay <cbeok@protonmail.com>
Date: Wed, 8 Jul 2020 19:43:55 -0500
Subject: added examples and readme

---
 examples.lisp | 74 ++++++++++++++++++++++++++++++++++++++++++++++++-----------
 1 file changed, 60 insertions(+), 14 deletions(-)

(limited to 'examples.lisp')

diff --git a/examples.lisp b/examples.lisp
index 2893447..83ba5c8 100644
--- a/examples.lisp
+++ b/examples.lisp
@@ -1,16 +1,59 @@
 (defpackage #:gtwiwtg.examples
   (:use #:cl #:gtwiwtg)
-  (:export #:perms #:all-primes))
+  (:export
+   #:perms
+   #:all-primes
+   #:fibs))
 
 (in-package :gtwiwtg.examples)
 
-;; permutations
+;;; PRIMES ;;; 
 
+(defun prime-p (n)
+  "Naive test for primes."
+  (loop
+     :for x :from 2 :upto (sqrt n)
+     :when (zerop (mod n x)) :do (return nil)
+     :finally (return t)))
+
+(defun all-primes ()
+  "Creates a generator that produces an infinite series of primes."
+  (filter! #'prime-p (range :from 2)))
+
+;; Here is an example of using all-primes to get a list of the 0th,
+;; 10th and 30th prime numbers, indexed starting at 0:
+
+(pick-out '(0 10 30) (all-primes)) ;; (2 31 127)
+
+;; Note that you can PICK-OUT in any order, and repeat too:
+(pick-out '(30 10 0 10) (all-primes)) ;; (127 31 2 31)
+
+;; get the 10 primes after the 20th prime
+
+(take 10 (skip! 20 (all-primes))) ;; (73 79 83 89 97 101 103 107 109 113)
+
+;;; FIBBONACCI NUMBERS ;;;
+
+(defun fibs ()
+  "Creates an infinite series of Fibbonacci numbers."
+  (from-recurrence
+   (lambda (n-1 n-2) (+ n-1 n-2))
+   1 0))
+
+;; First ten Fibbonacci numbers
+(take 10 (fibs)) ;; (1 2 3 5 8 13 21 34 55 89) 
+
+;; Just the 40th Fibbonacci number, indexed from 0
+(car (pick-out '(40) (fibs))) ;; 267914296
+
+
+;;; PERMUTATIONS ;;;
 
 (defun fill-and-insert (idx elem vec buffer)
   "A utilty function that modifies BUFFER. 
 
-The length of BUFFER is one greater than the length of VEC. 
+The length of BUFFER is assumed to be one greater than the length of
+VEC.
 
 This function fills the first IDX fields of BUFFER with the first IDX
 fields of VEC. Fills the field of BUFFER at IDX with ELEM.  Fills the
@@ -51,15 +94,18 @@ vector VEC, one at a time."
                                          :element-type (array-element-type vec)))))
         (inflate! (lambda (subperm) (thread-through elem subperm)) subperms))))
 
-;; primes
-
-(defun prime-p (n)
-  (loop
-     :for x :from 2 :upto (sqrt n)
-     :when (zerop (mod n x)) :do (return nil)
-     :finally (return t)))
-
-(defun all-primes ()
-  (filter! #'prime-p (range :from 1)))
-
+;; In the above, the interesting bit is in the recursive step, and in
+;; the call to inflate. Most of the noise in the above has to do with
+;; the creation of the displaced array (for memory conservation
+;; purposes) that is recursively apssed to perms.
 
+;; the whole thing could have been written:
+;;
+;; (defun perms (vec)
+;;   (if (= 1 (length vec)) (seq (list vec))
+;;       (let ((elem (elt vec 0))
+;;             (subperms (perms (subseq vec 1))))
+;;         (inflate! (lambda (subperm) (thread-through elem subperm))
+;;                   subperms))))
+;;
+;; which looks a little nicer but is less kind to the heap and to GC.
-- 
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