Add Monte Carlo implementation in Factor (#434)

* added Monte Carlo

* added USING statements so this can be run with no errors

* added pi calculation

* removed timing stuff

* add error

* aagh forgot again

Author: Nic Hartley

contents/monte_carlo_integration/code/factor/monte_carlo.factor

@@ -0,0 +1,21 @@
+USING: locals random math.ranges math.functions ;
+
+:: monte-carlo ( n in-shape?: ( x y -- ? ) -- % )
+  n <iota> [ drop random-unit random-unit in-shape? call ] count n /
+; inline
+
+! Use the monte-carlo approximation to calculate pi
+: monte-carlo-pi ( n -- pi-approx )
+  [ ! in-circle check
+    [ 2 ^ ] bi@ + ! get the distance from the center
+    1 <           ! see if it's less than the radius
+  ]
+  monte-carlo 4 * >float
+;
+
+USING: math.constants ;
+10000000 monte-carlo-pi ! Approximate pi
+dup .                   ! Print the approximation
+pi - pi / 100 * >float abs .  ! And the error margin
+
+

contents/monte_carlo_integration/monte_carlo_integration.md

@@ -71,6 +71,8 @@ each point is tested to see whether it's in the circle or not:
 [import:1-4, lang:"ruby"](code/ruby/monte_carlo.rb)
 {% sample lang="f90" %}
 [import:1-8, lang:"fortran"](code/fortran/monte_carlo.f90)
+{% sample lang="factor" %}
+[import:9-12 lang:"factor"](code/factor/monte_carlo.factor)
 {% sample lang="emojic" %}
 [import:23-27, lang:"emojicode"](code/emojicode/monte_carlo.emojic)
 {% sample lang="php" %}
@@ -155,6 +157,8 @@ Feel free to submit your version via pull request, and thanks for reading!
 [import, lang:"ruby"](code/ruby/monte_carlo.rb)
 {% sample lang="f90" %}
 [import, lang:"fortran"](code/fortran/monte_carlo.f90)
+{% sample lang="factor" %}
+[import, lang:"factor"](code/factor/monte_carlo.factor)
 {% sample lang="emojic" %}
 [import, lang:"emojicode"](code/emojicode/monte_carlo.emojic)
 {% sample lang="php" %}