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Ingy döt Net
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12390 changed files with 318560 additions and 27248 deletions
27
Task/Nth-root/Ada/nth-root.adb
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27
Task/Nth-root/Ada/nth-root.adb
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@ -0,0 +1,27 @@
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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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26
Task/Nth-root/AutoIt/nth-root.au3
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26
Task/Nth-root/AutoIt/nth-root.au3
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@ -0,0 +1,26 @@
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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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@ -1,13 +1,17 @@
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PROCEDURE nth
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PARAM N : INTEGER; A, P : REAL
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DIM N : INTEGER; A, P : REAL
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DIM TEMP0, TEMP1 : REAL
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A = 144.0
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P = 0.00001
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PRINT "Base: "; A
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PRINT "Number Root"
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FOR N = 1 TO 10
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TEMP0 := A
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TEMP1 := A/N
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WHILE ( abs(TEMP0 - TEMP1) > P) DO
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TEMP0 := TEMP1
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TEMP1 := (( N - 1.0) * TEMP1 + A / TEMP1 ^ (N - 1.0)) / N
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ENDWHILE
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PRINT "Root Number Precision"
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PRINT N, A, P
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PRINT "The Root is: ";TEMP1
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PRINT N, TEMP1
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NEXT N
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END
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100
Task/Nth-root/COBOL/nth-root.cob
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100
Task/Nth-root/COBOL/nth-root.cob
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@ -0,0 +1,100 @@
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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. Home Office.
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DATE-WRITTEN. 26 Mar 2026.
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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 initial value from console.
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**
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** Prints first ten roots.
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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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DATA DIVISION.
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WORKING-STORAGE SECTION.
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01 Num PIC 9(5).
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01 Loop PIC 9(5).
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01 Base PIC 9(5)V9(5).
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01 Z PIC 9(5)V9(5).
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01 Precision PIC 9V9(9).
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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 ZZZZ9.
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05 FILLER VALUE SPACES PIC X(8).
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05 Field2 PIC ZZZZ.ZZZZZZZZZ.
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01 HEADER.
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05 FILLER PIC X(72)
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VALUE " Number Root".
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PROCEDURE DIVISION.
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Main-Program.
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PERFORM FOREVER
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MOVE 0.000001 to Precision
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PERFORM Get-Input
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DISPLAY HEADER
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PERFORM VARYING Loop FROM 1 BY 1 UNTIL Loop = 10
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MOVE Loop TO Num
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PERFORM Compute-Root
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MOVE Num TO Field1
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MOVE TEMP1 TO Field2
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DISPLAY RESULTS
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END-PERFORM
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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 Base
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IF Base 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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Compute-Root.
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MOVE Base TO TEMP0
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DIVIDE Base BY Num GIVING TEMP1
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PERFORM WITH TEST AFTER UNTIL FUNCTION ABS(TEMP1 - TEMP0 )
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< Precision
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MOVE TEMP1 TO TEMP0
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COMPUTE TEMP1 = (( Num - 1.0) * TEMP1 + Base /
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TEMP1 ** (Num - 1.0)) / Num
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END-PERFORM.
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END-PROGRAM.
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<pre>
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Output:
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Input Base Number: 144
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Number Root
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1 144.000000000
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2 12.000000000
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3 5.241482788
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4 3.464101615
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5 2.701920077
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6 2.289428485
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7 2.033937009
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8 1.861209718
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9 1.737072938
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Input Base Number: 0
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Good Bye.
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</pre>
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@ -1,29 +1,27 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">pow_</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">e</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">x</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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with javascript_semantics
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function pow_(atom x, integer e)
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atom r = 1
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for i=1 to e do
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r *= x
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end for
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return r
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">nth_root</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">eps</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1e-15</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- relative accuracy</span>
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<span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">while</span> <span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
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<span style="color: #000080;font-style:italic;">-- atom d = ( y / power(x,n-1) - x ) / n</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">pow_</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">n</span>
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<span style="color: #000000;">x</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">d</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">eps</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span> <span style="color: #000080;font-style:italic;">-- absolute accuracy </span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">></span> <span style="color: #0000FF;">-</span><span style="color: #000000;">e</span> <span style="color: #008080;">and</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">e</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">x</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function nth_root(atom y, n)
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atom eps = 1e-15, -- relative accuracy
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x = 1
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while 1 do
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-- atom d = ( y / power(x,n-1) - x ) / n
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atom d = ( y / pow_(x,n-1) - x ) / n
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x += d
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atom e = eps*x -- absolute accuracy
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if d > -e and d < e then exit end if
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end while
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return x
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end function
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">yn</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">yn</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"nth_root(%d,%d) = %.10g, builtin = %.10g\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nth_root</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)})</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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<span style="color: #7060A8;">papply</span><span style="color: #0000FF;">({{</span><span style="color: #000000;">1024</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">27</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5642</span><span style="color: #0000FF;">,</span><span style="color: #000000;">125</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">4913</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">125</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1000000000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">test</span><span style="color: #0000FF;">)</span>
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<!--
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procedure test(sequence yn)
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atom {y,n} = yn
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printf(1,"nth_root(%d,%d) = %.10g, builtin = %.10g\n",{y,n,nth_root(y,n),power(y,1/n)})
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end procedure
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papply({{1024,10},{27,3},{2,2},{5642,125},{4913,3},{8,3},{16,2},{16,4},{125,3},{1000000000,3},{1000000000,9}},test)
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39
Task/Nth-root/PowerShell/nth-root.ps1
Normal file
39
Task/Nth-root/PowerShell/nth-root.ps1
Normal file
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@ -0,0 +1,39 @@
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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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@ -1,35 +1,29 @@
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program nth
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#
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integer root
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integer n
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real number, precision
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real temp0, temp1
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1 format('Enter the base number: ')
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2 format('Enter the desired root: ')
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3 format('Enter the desired precision: ')
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4 format(F12.6)
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5 format(I6)
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write(6,1)
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read(5,4)number
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write(6,2)
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read(5,5)root
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write(6,3)
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read(5,4)precision
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6 format(' number root')
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7 format(i6,f12.6)
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precision=0.00001
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root=1.0
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number=144.0
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n=10
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write(6,6)
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for (i=1;i<=n;i=i+1) {
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temp0 = number
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temp1 = number/root
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temp1 = number/i
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while ( abs(temp0 - temp1) > precision )
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while ( abs(temp1 - temp0) > precision )
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{
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temp0 = temp1
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temp1 = ((root - 1.0) * temp1 + number / temp1 ** (root - 1.0)) / root
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temp1 = ((i - 1.0) * temp1 + number / temp1 ** (i - 1.0)) / i
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}
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6 format(' number root precision')
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write(6,6)
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7 format(f12.6,i6,f12.6)
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write (6,7)number,root,precision
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8 format('The root is: ',F12.6)
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write (6,8)temp1
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write (6,7)i,temp1
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}
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end
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