Add approximate counting algorithm in Emacs Lisp

.editorconfig

@@ -51,6 +51,11 @@ indent_size = 4
 indent_style = space
 indent_size = 2
 
+# Emacs Lisp
+[*.el]
+indent_style = space
+indent_size = 2
+
 # Emojicode
 [*.emojic]
 indent_style = space

book.json

@@ -102,6 +102,10 @@
           "lang": "elm",
           "name": "Elm"
         },
+        {
+          "lang": "elisp",
+          "name": "Emacs Lisp"
+        },
         {
           "lang": "LabVIEW",
           "name": "LabVIEW"

contents/approximate_counting/approximate_counting.md

@@ -366,6 +366,8 @@ As we do not have any objects to count, we will instead simulate the counting wi
 [import, lang:"cpp"](code/c++/approximate_counting.cpp)
 {% sample lang="python" %}
 [import, lang:"python"](code/python/approximate_counting.py)
+{% sample lang="elisp" %}
+[import, lang:"elisp"](code/elisp/approximate-counting.el)
 {% endmethod %}
 
 ### Bibliography

contents/approximate_counting/code/elisp/approximate-counting.el

@@ -0,0 +1,43 @@
+(require 'cl-extra)
+
+(defun sum (things)
+  "Return the sum of all THINGS."
+  (apply '+ things))
+
+(defun n (v a)
+  "Return the approximate count at a given register value V.
+A is a scaling value for the logarithm based on Morris' paper."
+  (* a (- (expt (+ 1 (/ 1 (float a))) v) 1)))
+
+(defun increment (v a)
+  "Return V, randomly incremented by one or as-is.
+A is a scaling value for the logarithm based on Morris' paper."
+  (let ((delta (/ 1 (- (n (1+ v) a) (n v a)))))
+    (if (<= (cl-random 1.0) delta)
+        (1+ v)
+      v)))
+
+(defun approximate-count (nitems a)
+  "Simulate the counting of NITEMS, returning an approximate count.
+A is a scaling value for the logarithm based on Morris' paper."
+  (let ((v 0))
+    (dotimes (i nitems)
+      (setq v (increment v a)))
+    (n v a)))
+
+(defun test-approximate-count (ntrials nitems a threshold)
+  "Test approximate counting, printing when passing.
+NITEMS items are counted for NTRIALS trials to within a THRESHOLD error
+(float between 0 and 1).
+A is a scaling value for the logarithm based on Morris' paper."
+  (let* ((samples (mapcar (lambda (x) (approximate-count nitems a)) (number-sequence 1 ntrials)))
+         (avg (/ (sum samples) ntrials)))
+    (if (< (abs (/ (- avg nitems) nitems)) threshold)
+        (princ "passed\n"))))
+
+(princ "testing 1,000, a = 30, 1% error\n")
+(test-approximate-count 100 1000 30 0.1)
+(princ "testing 12,345, a = 10, 1% error\n")
+(test-approximate-count 100 12345 10 0.1)
+(princ "testing 222,222, a = 0.5, 10% error\n")
+(test-approximate-count 100 222222 0.5 0.2)