Lisp Monte Carlo (#514)

* First working version of monte carlo integration in lisp

* Forgot to add docstring

* Added error output.

* Updated the output

Author: Trashtalk217

contents/monte_carlo_integration/code/lisp/monte-carlo.lisp

@@ -0,0 +1,18 @@
+;;;; Monte carlo integration to approximate pi
+
+(defun in-circle-p (x y)
+  "Checks if a point is in a unit circle"
+  (< (+ (* x x) (* y y)) 1))
+
+(defun monte-carlo (samples)
+  "Returns an approximation of pi"
+  (loop repeat samples
+    with count = 0 
+    do
+      (when (in-circle-p (random 1.0) (random 1.0))
+            (incf count))
+    finally (return (* (/ count samples) 4.0))))
+
+(defvar pi-estimate (monte-carlo 5000000))
+(format t "Estimate: ~D ~%" pi-estimate)
+(format t "Error: ~D%" (* (/ (abs (- pi-estimate pi)) pi) 100))

contents/monte_carlo_integration/monte_carlo_integration.md

@@ -81,6 +81,8 @@ each point is tested to see whether it's in the circle or not:
 [import:2-4, lang:"lisp"](code/racket/monte_carlo.rkt)
 {% sample lang="scala" %}
 [import:3-3, lang:"scala"](code/scala/monte_carlo.scala)
+{% sample lang="lisp" %}
+[import:3-5, lang:"lisp"](code/scala/monte-carlo.lisp)
 {% sample lang="asm-x64" %}
 [import:21-32, lang:"asm-x64"](code/asm-x64/monte_carlo.s)
 {% endmethod %}
@@ -163,6 +165,8 @@ Feel free to submit your version via pull request, and thanks for reading!
 [import, lang:"lisp"](code/racket/monte_carlo.rkt)
 {% sample lang="scala" %}
 [import, lang:"scala"](code/scala/monte_carlo.scala)
+{% sample lang="lisp" %}
+[import, lang:"lisp"](code/scala/monte-carlo.lisp)
 {% sample lang="asm-x64" %}
 [import, lang:"asm-x64"](code/asm-x64/monte_carlo.s)
 {% endmethod %}