Added monte carlo in bash (#519)

Author: Ariana1729

contents/monte_carlo_integration/code/bash/monte_carlo.bash

@@ -0,0 +1,26 @@
+#!/usr/bin/env bash
+inCircle() {
+    local ret
+    local mag
+    ((ret = 0))
+    if (($1 ** 2 + $2 ** 2 < 1073676289)); then # 1073676289 = 32767 ** 2
+        ((ret = 1))
+    fi
+    printf "%d" $ret
+}
+
+monteCarlo() {
+    local count
+    local i
+    ((count = 0))
+    for ((i = 0; i < $1; i++)); do
+        if (($(inCircle RANDOM RANDOM) == 1)); then
+            ((count++))
+        fi
+    done
+    echo "scale = 8; 4 * $count / $1" | bc
+}
+
+est=$(monteCarlo 10000)
+echo "The estimate of pi is $est"
+echo "Percentage error: $(echo "scale = 8; 100 * sqrt( ( 1 - $est / (4*a(1)) ) ^ 2 )" | bc -l)"

contents/monte_carlo_integration/monte_carlo_integration.md

@@ -87,6 +87,8 @@ each point is tested to see whether it's in the circle or not:
 [import:3-5, lang:"lisp"](code/clisp/monte-carlo.lisp)
 {% sample lang="asm-x64" %}
 [import:21-32, lang:"asm-x64"](code/asm-x64/monte_carlo.s)
+{% sample lang="bash" %}
+[import:2-10, lang:"bash"](code/bash/monte_carlo.bash)
 {% endmethod %}
 
 If it's in the circle, we increase an internal count by one, and in the end,
@@ -173,6 +175,8 @@ Feel free to submit your version via pull request, and thanks for reading!
 [import, lang:"lisp"](code/clisp/monte-carlo.lisp)
 {% sample lang="asm-x64" %}
 [import, lang:"asm-x64"](code/asm-x64/monte_carlo.s)
+{% sample lang="bash" %}
+[import, lang:"bash"](code/bash/monte_carlo.bash)
 {% endmethod %}