Data update
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Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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with Ada.Text_IO; use Ada.Text_IO;
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procedure Test_Nth_Root is
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generic
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type Real is digits <>;
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function Nth_Root (Value : Real; N : Positive) return Real;
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function Nth_Root (Value : Real; N : Positive) return Real is
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type Index is mod 2;
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X : array (Index) of Real := (Value, Value);
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K : Index := 0;
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begin
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loop
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X (K + 1) := ( (Real (N) - 1.0) * X (K) + Value / X (K) ** (N-1) ) / Real (N);
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exit when X (K + 1) >= X (K);
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K := K + 1;
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end loop;
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return X (K + 1);
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end Nth_Root;
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function Long_Nth_Root is new Nth_Root (Long_Float);
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begin
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Put_Line ("1024.0 10th =" & Long_Float'Image (Long_Nth_Root (1024.0, 10)));
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Put_Line (" 27.0 3rd =" & Long_Float'Image (Long_Nth_Root (27.0, 3)));
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Put_Line (" 2.0 2nd =" & Long_Float'Image (Long_Nth_Root (2.0, 2)));
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Put_Line ("5642.0 125th =" & Long_Float'Image (Long_Nth_Root (5642.0, 125)));
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end Test_Nth_Root;
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@ -1,26 +0,0 @@
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;AutoIt Version: 3.2.10.0
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$A=4913
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$n=3
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$x=20
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ConsoleWrite ($n& " root of "& $A & " is " &nth_root_it($A,$n,$x))
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ConsoleWrite ($n& " root of "& $A & " is " &nth_root_rec($A,$n,$x))
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;Iterative
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Func nth_root_it($A,$n,$x)
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$x0="0"
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While StringCompare(string($x0),string($x))
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ConsoleWrite ($x&@CRLF)
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$x0=$x
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$x=((($n-1)*$x)+($A/$x^($n-1)))/$n
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WEnd
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Return $x
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EndFunc
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;Recursive
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Func nth_root_rec($A,$n,$x)
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ConsoleWrite ($x&@CRLF)
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If $x==((($n-1)*$x)+($A/$x^($n-1)))/$n Then
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Return $x
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EndIf
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Return nth_root_rec($A,$n,((($n-1)*$x)+($A/$x^($n-1)))/$n)
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EndFunc
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@ -1,98 +0,0 @@
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IDENTIFICATION DIVISION.
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PROGRAM-ID. Nth-Root.
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AUTHOR. Bill Gunshannon.
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INSTALLATION.
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DATE-WRITTEN. 4 Feb 2020.
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************************************************************
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** Program Abstract:
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** Compute the Nth Root of a positive real number.
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**
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** Takes values from console. If Precision is left
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** blank defaults to 0.001.
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**
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** Enter 0 for first value to terminate program.
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************************************************************
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ENVIRONMENT DIVISION.
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INPUT-OUTPUT SECTION.
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FILE-CONTROL.
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SELECT Root-File ASSIGN TO "Root-File"
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ORGANIZATION IS LINE SEQUENTIAL.
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DATA DIVISION.
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FILE SECTION.
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FD Root-File
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DATA RECORD IS Parameters.
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01 Parameters.
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05 Root PIC 9(5).
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05 Num PIC 9(5)V9(5).
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05 Precision PIC 9V9(9).
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WORKING-STORAGE SECTION.
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01 TEMP0 PIC 9(9)V9(9).
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01 TEMP1 PIC 9(9)V9(9).
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01 RESULTS.
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05 Field1 PIC ZZZZZ.ZZZZZ.
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05 FILLER PIC X(5).
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05 Field2 PIC ZZZZ9.
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05 FILLER PIC X(14).
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05 Field3 PIC 9.999999999.
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01 HEADER.
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05 FILLER PIC X(72)
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VALUE " Number Root Precision.".
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01 Disp-Root PIC ZZZZZ.ZZZZZ.
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PROCEDURE DIVISION.
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Main-Program.
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PERFORM FOREVER
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PERFORM Get-Input
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IF Precision = 0.0
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THEN MOVE 0.001 to Precision
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END-IF
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PERFORM Compute-Root
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MOVE Root TO Field2
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MOVE Num TO Field1
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MOVE Precision TO Field3
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DISPLAY HEADER
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DISPLAY RESULTS
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DISPLAY " "
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MOVE TEMP1 TO Disp-Root
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DISPLAY "The Root is: " Disp-Root
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END-PERFORM.
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Get-Input.
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DISPLAY "Input Base Number: " WITH NO ADVANCING
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ACCEPT Num
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IF Num EQUALS ZERO
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THEN
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DISPLAY "Good Bye."
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STOP RUN
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END-IF
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DISPLAY "Input Root: " WITH NO ADVANCING
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ACCEPT Root
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DISPLAY "Input Desired Precision: " WITH NO ADVANCING
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ACCEPT Precision.
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Compute-Root.
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MOVE Root TO TEMP0
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DIVIDE Num BY Root GIVING TEMP1
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PERFORM UNTIL FUNCTION ABS(TEMP0 - TEMP1)
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LESS THAN Precision
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MOVE TEMP1 TO TEMP0
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COMPUTE TEMP1 = (( Root - 1.0) * TEMP1 + Num /
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TEMP1 ** (Root - 1.0)) / Root
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END-PERFORM.
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END-PROGRAM.
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@ -1,39 +0,0 @@
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#NoTeS: This sample code does not validate inputs
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# Thus, if there are errors the 'scary' red-text
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# error messages will appear.
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#
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# This code will not work properly in floating point values of n,
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# and negative values of A.
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#
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# Supports negative values of n by reciprocating the root.
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$epsilon=1E-10 #Sample Epsilon (Precision)
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function power($x,$e){ #As I said in the comment
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$ret=1
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for($i=1;$i -le $e;$i++){
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$ret*=$x
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}
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return $ret
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}
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function root($y,$n){ #The main Function
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if (0+$n -lt 0){$tmp=-$n} else {$tmp=$n} #This checks if n is negative.
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$ans=1
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do{
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$d = ($y/(power $ans ($tmp-1)) - $ans)/$tmp
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$ans+=$d
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} while ($d -lt -$epsilon -or $d -gt $epsilon)
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if (0+$n -lt 0){return 1/$ans} else {return $ans}
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}
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#Sample Inputs
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root 625 2
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root 2401 4
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root 2 -2
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root 1.23456789E-20 34
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root 9.87654321E20 10 #Quite slow here, I admit...
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((root 5 2)+1)/2 #Extra: Computes the golden ratio
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((root 5 2)-1)/2
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@ -1,5 +1,5 @@
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-- 8 May 2025
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include Settings
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-- 24 Aug 2025
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include Setting
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say 'NTH ROOT'
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say version
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@ -18,7 +18,4 @@ say 'digits = ' digs
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say 'answer = ' Nroot(x,root)
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exit
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include Numbers
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include Functions
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include Constants
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include Abend
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include Math
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