Data update

Task/Nth-root/EMal/nth-root.emal

@@ -0,0 +1,12 @@
+fun nthRoot ← real by real n, real x, real precision
+  Pair result ← real%real(x ⇒ x / n).named("previous", "current")
+  while abs(result.current - result.previous) > precision
+    result.previous ← result.current
+    result.current ← ( (n - 1) * result.current + x / result.current ** (n - 1) ) / n
+  end
+  return result.current
+end
+writeLine("{ \"nthroot\": ", nthRoot(2, 152.2756, 0.00000000000001), ", \"builtin\": ", √152.2756, " }")
+writeLine("{ \"nthroot\": ", nthRoot(5, 34.0, 0.00000000000001), ", \"builtin\": ", 5 // 34.0, " }")
+writeLine("{ \"nthroot\": ", nthRoot(10, 42.0, 0.00000000000001), ", \"builtin\": ", 10 // 42.0, " }")
+writeLine("{ \"nthroot\": ", nthRoot(0.5, 7.0, 0.000000000001), ", \"builtin\": ", 0.5 // 7, " }")

Task/Nth-root/REXX/nth-root-2.rexx

@@ -0,0 +1,4 @@
+do until old=g;   old=g              /*where da rubber meets da road-+*/<br>
+g=format((rm*g**r+x)/r/g**rm,, d-2)  /* ?------ the root computation-+*/<br>
+'''say 'g' g 'old' old'''<br>
+end   /*until old=g*/                /*maybe until the cows come home.*/<br>

Task/Nth-root/REXX/nth-root-3.rexx

@@ -0,0 +1,60 @@
+/*REXX program calculates the  Nth root  of  X,  with  DIGS  (decimal digits) accuracy. */
+include Settings
+
+say version; say 'Nth root'; say
+parse arg x root digs .                          /*obtain optional arguments from the CL*/
+if    x=='' |    x==","   then    x= 2           /*Not specified?  Then use the default.*/
+if root=='' | root==","   then root= 2           /* "       "        "   "   "      "   */
+if digs=='' | digs==","   then digs=65           /* "       "        "   "   "      "   */
+numeric digits digs                              /*set the  decimal digits  to   DIGS.  */
+say '       x = '    x                           /*echo the value of   X.               */
+say '    root = '    root                        /*  "   "    "    "   ROOT.            */
+say '  digits = '    digs                        /*  "   "    "    "   DIGS.            */
+say '  answer = '    nroot(x, root)              /*show the value of   ANSWER.          */
+exit                                             /*stick a fork in it,  we're all done. */
+/*--------------------------------------------------------------------------------------*/
+Nroot:
+/* Nth root function = x^(1/n) */
+procedure expose glob.
+arg x,n
+/* Fast values */
+if x = 0 then
+   return 0
+if x = 1 then
+   return 1
+/* Formulas using faster methods */
+if n = 2 then
+   return Sqrt(x)
+if n = 3 then
+   return Cbrt(x)
+if n = 4 then
+   return Qtrt(x)
+/* Calculate */
+sx = Sign(x); x = Abs(x)
+p1 = Digits(); p2 = p1+2
+numeric digits 3
+/* First guess low accuracy */
+y = 1/Exp(Ln(x)/n)
+numeric digits p2
+/* Dynamic precision */
+d = p2
+do k = 1 while d > 4
+   d.k = d; d = d%2+1
+end
+d.k = 4
+/* Halley */
+a = 1/n; b = n+1
+do j = k to 1 by -1
+   numeric digits d.j
+   y = y*a*(b-x*y**n)
+end
+y = 1/y
+if sx < 0 then
+   y = -y
+numeric digits p1
+return y+0
+
+include Numbers
+include Functions
+include Constants
+include Abend