Data update

Task/Nth-root/Bracmat/nth-root-2.bracmat

@@ -0,0 +1,51 @@
+  "The body of Pow will be compiled twice: once as the the code hidden in the
+   UFP object called 'POW' (see below) and once as a local function of the code
+   hidden in the UFP object called 'Root' (also see below)."
+& ( Pow
+  =   (s.x) (s.e)
+    .   1:?r
+      & 0:?i
+      &   whl
+        ' ( !i:<!e
+          & !x*!r:?r
+          & 1+!i:?i
+          )
+      & !r
+  )
+& "The next expression is a macro expression that expands $Pow to the body of
+   the Pow function defined above.
+   There is another local function, called 'even'."
+&
+    ' ( (s.n) (s.x)
+      .   (Pow=$Pow)
+        & ( even
+          =   (s.v)
+            .   floor$(!v*1/2):?v/2
+              & subtract$(!v,2*!v/2)
+          )
+        & ( !x:0
+          |   ( !n:<1
+              | !x:<0&even$!n:0
+              )
+            & divide$(0,0)
+          |   0x1p-52*10:?EPS
+            & 0x1p-52*-10:?EPS-
+            & 1:?r
+            & !n+-1:?n-1
+            &   whl
+              ' (     divide
+                    $ (divide$(!x,Pow$(!r,!n-1))+-1*!r,!n)
+                  : ?d
+                & !d+!r:?r
+                & (!d:~<!EPS|!d:~>!EPS-)
+                )
+            & !r
+          )
+      )
+  : (=?root)
+& "Create two UFP objects, POW and ROOT. They are each others' inverse."
+& new$(UFP,Pow):?POW
+& new$(UFP,root):?Root
+& 15:?n
+& (POW..go)$("-3.14159",15):?x
+& out$((Root..go)$(!n,!x));

Task/Nth-root/Raku/nth-root.raku

@@ -1,11 +1,7 @@
-sub nth-root ($n, $A, $p=1e-9)
-{
-    my $x0 = $A / $n;
-    loop {
-        my $x1 = (($n-1) * $x0 + $A / ($x0 ** ($n-1))) / $n;
-        return $x1 if abs($x1-$x0) < abs($x0 * $p);
-        $x0 = $x1;
-    }
+sub infix:<√>($n, $A) {
+    .tail given $A / $n, { (($n-1) * $_+ $A / ($_** ($n-1))) / $n } ... * ≅ *;
 }
 
-say nth-root(3,8);
+use Test;
+plan 9;
+is-approx ($_√pi)**$_, pi for 2 .. 10;