September 2017 Update

Task/Ackermann-function/Jq/ackermann-function-4.jq

@@ -0,0 +1,29 @@
+# input: [m,n, cache]
+# output [value, updatedCache]
+def ack:
+
+  # input: [value,cache]; output: [value, updatedCache]
+  def cache(key): .[1] += { (key): .[0] };
+
+  def pow2: reduce range(0; .) as $i (1; .*2);
+
+  .[0] as $m | .[1] as $n | .[2] as $cache
+  | if   $m == 0 then [$n + 1, $cache]
+    elif $m == 1 then [$n + 2, $cache]
+    elif $m == 2 then [2 * $n + 3, $cache]
+    elif $m == 3 then [8 * ($n|pow2) - 3, $cache]
+    else
+    (.[0:2]|tostring) as $key
+    | $cache[$key] as $value
+    | if $value then [$value, $cache]
+      elif $n == 0 then
+        ([$m-1, 1, $cache] | ack)
+        | cache($key)
+      else
+        ([$m, $n-1, $cache ] | ack)
+        | [$m-1, .[0], .[1]] | ack
+        | cache($key)
+      end
+    end;
+
+def A(m;n): [m,n,{}] | ack | .[0];