Add pi approximation as an example

examples/pi-approx.ang

@@ -0,0 +1,48 @@
+# This program computes an approximation of pi using the proof
+# of the basel problem. It requires many terms to calculate a
+# good approximation.
+# see: https://en.wikipedia.org/wiki/Basel_problem
+
+# The amount of terms
+terms := 10000
+
+# The running sum of terms
+tot := 0
+
+n := 1
+while n <= terms {
+	tot = tot + 1 / (n*n)
+	n = n + 1
+}
+
+tot = tot * 6
+
+# get the absolute value of a number
+func abs(x) {
+	if x < 0 {
+		return -x
+	}
+	return x
+}
+
+# calculate an approximation of the square root of tot using
+# newton's method.
+# see: https://en.wikipedia.org/wiki/Newton's_method
+# The required accuracy
+SQRT_ACC := 0.00001
+func sqrt(x) {
+    pg := 0 # previous guess
+    g := 1 # current guess
+
+    while abs(pg - g) >= SQRT_ACC {
+        pg = g
+        g = (pg + tot/pg)/2
+    }
+
+    return g
+}
+
+tot = sqrt(tot)
+
+# output the result
+write(tot)