Data update

Task/Nth-root/AWK/nth-root-2.awk

@@ -0,0 +1,24 @@
+#!/usr/bin/awk -f
+BEGIN {
+    # test
+	print nthroot(8,3)
+	print nthroot(16,2)
+	print nthroot(16,4)
+	print nthroot(125,3)
+	print nthroot(3,3)
+	print nthroot(3,2)
+}
+
+function nthroot(a, n,   x, y, a_n, n1_n) {
+	# no need for eps, the values are monotonically decreasing
+	# until the root is found (if the initial value is above the root)
+    x = 1 + a / n 				# starting value above the root
+    a_n = a/n					# precompute loop invariants
+    n1_n = (n - 1) / n
+	do {
+		y = x
+		x  = n1_n * x + a_n / x^(n-1)
+	}  while (x < y)
+	# no harm to use average if x = y
+	return (x + y) / 2
+}

Task/Nth-root/AWK/nth-root-3.awk

@@ -0,0 +1,8 @@
+{
+  x = $0
+  do {
+	y = x
+	x = (x + $0/x)/2
+  } while (x < y)
+  print "sqrt(" a ")=" x
+}