Square root by hand

Square root by hand is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Create a program that will calculate n digits of the square root of a number.

The program should continue forever (or until the number of digits is specified) calculating and outputting each decimal digit in succession. The program should be a "spigot algorithm" generating the digits of the number sequentially from left to right providing increasing precision as the algorithm proceeds.

C#

Translation of: Visual Basic .NET

Library: System.Numerics

<lang csharp>using System; using static System.Math; using static System.Console; using BI = System.Numerics.BigInteger;

class Program {

   static void Main(string[] args) {
       BI i, j, k, d; i = 2; int n = -1; int n0 = -1;
       j = (BI)Floor(Sqrt((double)i)); k = j; d = j;
       DateTime st = DateTime.Now;
       if (args.Length > 0) int.TryParse(args[0], out n);
       if (n > 0) n0 = n; else n = 1;
       do {
           Write(d); i = (i - k * d) * 100; k = 20 * j;
           for (d = 1; d <= 10; d++)
               if ((k + d) * d > i) { d -= 1; break; }
           j = j * 10 + d; k += d; if (n0 > 0) n--;
       } while (n > 0);
       if (n0 > 0) WriteLine("\nTime taken for {0} digits: {1}", n0, DateTime.Now - st); }

}</lang>

Output:

14142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372
Time taken for 500 digits: 00:00:00.0092331

Go

Translation of: Visual Basic .NET

<lang go>package main

import (

   "fmt"
   "math/big"

)

var one = big.NewInt(1) var ten = big.NewInt(10) var twenty = big.NewInt(20) var hundred = big.NewInt(100)

func sqrt(n int64, limit int) {

   i := big.NewInt(n)
   j := new(big.Int).Sqrt(i)
   k := new(big.Int).Set(j)
   d := new(big.Int).Set(j)
   t := new(big.Int)
   digits := 0
   for digits < limit {
       fmt.Print(d)
       t.Mul(k, d)
       i.Sub(i, t)
       i.Mul(i, hundred)
       k.Mul(j, twenty)
       d.Set(one)
       for d.Cmp(ten) <= 0 {
           t.Add(k, d)
           t.Mul(t, d)
           if t.Cmp(i) > 0 {
               d.Sub(d, one)
               break
           }
           d.Add(d, one)
       }
       j.Mul(j, ten)
       j.Add(j, d)
       k.Add(k, d)
       digits = digits + 1
   }
   fmt.Println()

}

func main() {

   sqrt(2, 480) // enough for demo purposes

}</lang>

Output:

141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871

Visual Basic .NET

Library: System.Numerics

This is "spigot like", but not a true spigot, just an implementation of the "by hand" method of computing the square root, in this case, of two.<lang vbnet>Imports System.Math, System.Console, BI = System.Numerics.BigInteger

Module Module1

   Sub Main(ByVal args As String())
       Dim i, j, k, d As BI : i = 2
       j = CType(Floor(Sqrt(CDbl(i))), BI) : k = j : d = j
       Dim n As Integer = -1, n0 As Integer = -1,
           st As DateTime = DateTime.Now
       If args.Length > 0 Then Integer.TryParse(args(0), n)
       If n > 0 Then n0 = n Else n = 1
       Do
           Write(d) : i = (i - k * d) * 100 : k = 20 * j
           For d = 1 To 10
               If (k + d) * d > i Then d -= 1 : Exit For
           Next
           j = j * 10 + d : k += d : If n0 > 0 Then n = n - 1
       Loop While n > 0
       If n0 > 0 Then WriteLine (VbLf & "Time taken for {0} digits: {1}", n0, DateTime.Now - st)
   End Sub

End Module</lang>

Output:

Execute without any command line parameters for it to run until it crashes (due to BigInteger variables eating up available memory). Output with command line parameter of 500:

14142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471603868999706990048150305440277903164542478230684929369186215805784631115966687130130156185689872372
Time taken for 500 digits: 00:00:00.0263710

Wren

Translation of: Visual Basic .NET

Library: Wren-big

<lang ecmascript>import "/big" for BigInt

var sqrt = Fn.new { |n, limit|

   var i = BigInt.new(n)
   var j = i.isqrt
   var k = j
   var d = j
   var digits = 0
   while (digits < limit) {
       System.write(d)
       i = (i - k*d) * 100
       k = j * 20
       d = BigInt.one
       while (d <= 10) {
           if ((k + d)*d > i) {
               d = d.dec
               break
           }
           d = d.inc
       }
       j = j*10 + d
       k = k + d
       digits = digits + 1
   }
   System.print()

}

sqrt.call(2, 480) // enough for demo purposes</lang>

Output:

141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871