September 2017 Update

Task/Nth-root/Bc/nth-root.bc

@@ -0,0 +1,30 @@
+/* Take the nth root of 'a' (a positive real number).
+ * 'n' must be an integer.
+ * Result will have 'd' digits after the decimal point.
+ */
+define r(a, n, d) {
+    auto e, o, x, y, z
+
+    if (n == 0) return(1)
+    if (a == 0) return(0)
+
+    o = scale
+    scale = d
+    e = 1 / 10 ^ d
+
+    if (n < 0) {
+        n = -n
+        a = 1 / a
+    }
+
+    x = 1
+    while (1) {
+        y = ((n - 1) * x + a / x ^ (n - 1)) / n
+        z = x - y
+        if (z < 0) z = -z
+        if (z < e) break
+        x = y
+    }
+    scale = o
+    return(y)
+}

Task/Nth-root/Kotlin/nth-root.kotlin

@@ -0,0 +1,21 @@
+// version 1.0.6
+
+fun nthRoot(x: Double, n: Int): Double {
+    if (n < 2) throw IllegalArgumentException("n must be more than 1")
+    if (x <= 0.0) throw IllegalArgumentException("x must be positive")
+    val np = n - 1
+    fun iter(g: Double) = (np * g + x / Math.pow(g, np.toDouble())) / n
+    var g1 = x
+    var g2 = iter(g1)
+    while (g1 != g2) {
+        g1 = iter(g1)
+        g2 = iter(iter(g2))
+    }
+    return g1
+}
+
+fun main(args: Array<String>) {
+   val numbers = arrayOf(1728.0 to 3, 1024.0 to 10, 2.0 to 2)
+   for (number in numbers)
+       println("${number.first} ^ 1/${number.second}\t = ${nthRoot(number.first, number.second)}")
+}

Task/Nth-root/Lua/nth-root.lua

@@ -1,3 +1,3 @@
-function nth_root(num,root)
+function nroot(root, num)
   return num^(1/root)
 end

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)

Task/Nth-root/SPL/nth-root.spl

@@ -0,0 +1,14 @@
+nthr(n,r) <= n^(1/r)
+
+nthroot(n,r)=
+  a = n/r
+  g = n
+  > g!=a
+    g = a
+    a = (1/r)*(((r-1)*g)+(n/(g^(r-1))))
+  <
+  <= a
+.
+
+#.output(nthr(2,2))
+#.output(nthroot(2,2))

Task/Nth-root/Zkl/nth-root.zkl

@@ -0,0 +1,11 @@
+fcn nthroot(nth,a,precision=1.0e-5){
+   x:=prev:=a=a.toFloat(); n1:=nth-1;
+   do{
+      prev=x;
+      x=( prev*n1 + a/prev.pow(n1) ) / nth;
+   }
+   while( not prev.closeTo(x,precision) );
+   x
+}
+
+nthroot(5,34) : "%.20f".fmt(_).println()  # => 2.02439745849988828041