Data update

Task/Monte-Carlo-methods/DuckDB/monte-carlo-methods.duckdb

@@ -0,0 +1,20 @@
+create or replace function mcPi(n) as (
+  with recursive cte as (
+    select -1 as i, 0 as count, NULL::DOUBLE as x, NULL::DOUBLE as y
+    union all
+    select i+1 as i,
+           count + if( x*x + y*y <= 1, 1, 0) as count,
+           random() as x,
+           random() as y
+      from cte
+      where i < n
+   )
+   select last( 4 * count / n order by i)
+   from cte
+);
+
+# Examples:
+
+select n, mcPi, format('{:.5f}', (mcPi - pi()) / pi()) as "relative error"
+from (select n, mcPi(n) as mcPi
+      from (select unnest([100, 1000, 10000, 100000, 200000]) as n));