September 2017 Update

Task/Nth-root/Phix/nth-root.phix

@@ -0,0 +1,33 @@
+function pow_(atom x, integer e)
+    atom r = 1
+    for i=1 to e do
+        r *= x
+    end for
+    return r
+end function
+
+function nth_root(atom y,n)
+atom eps = 1e-15   -- relative accuracy
+atom x = 1
+    while 1 do
+--      atom d = ( y / power(x,n-1) - x ) / n
+        atom d = ( y / pow_(x,n-1) - x ) / n
+        x += d
+        atom e = eps*x   -- absolute accuracy
+        if d > -e and d < e then exit end if
+    end while
+    return {y,n,x,power(y,1/n)}
+end function
+
+?nth_root(1024,10)
+?nth_root(27,3)
+?nth_root(2,2)
+?nth_root(5642,125)
+--?nth_root(7,0.5)  -- needs power(), not pow_()
+?nth_root(4913,3)
+?nth_root(8,3)
+?nth_root(16,2)
+?nth_root(16,4)
+?nth_root(125,3)
+?nth_root(1000000000,3)
+?nth_root(1000000000,9)