Data update
This commit is contained in:
Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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@ -1,76 +0,0 @@
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with Ada.Text_IO; with Ada.Integer_Text_IO;
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with Ada.Strings.Fixed;
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procedure Totient is
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function Totient (N : in Integer) return Integer is
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Tot : Integer := N;
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I : Integer;
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N2 : Integer := N;
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begin
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I := 2;
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while I * I <= N2 loop
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if N2 mod I = 0 then
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while N2 mod I = 0 loop
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N2 := N2 / I;
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end loop;
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Tot := Tot - Tot / I;
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end if;
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if I = 2 then
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I := 1;
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end if;
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I := I + 2;
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end loop;
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if N2 > 1 then
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Tot := Tot - Tot / N2;
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end if;
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return Tot;
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end Totient;
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Count : Integer := 0;
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Tot : Integer;
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Placeholder : String := " n Phi Is_Prime";
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Image_N : String renames Placeholder ( 1 .. 3);
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Image_Phi : String renames Placeholder ( 6 .. 8);
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Image_Prime : String renames Placeholder (11 .. Placeholder'Last);
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use Ada.Text_IO;
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use Ada.Integer_Text_IO;
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Last : constant := 25;
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begin
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Put_Line (Placeholder);
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for N in 1 .. Last loop
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Tot := Totient (N);
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if N - 1 = Tot then
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Count := Count + 1;
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end if;
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Put (Image_N, N);
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Put (Image_Phi, Tot);
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Image_Prime := Ada.Strings.Fixed.Tail
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(Source => (if N - 1 = Tot then True'Image else False'Image),
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Count => Image_Prime'Length);
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Put_Line (Placeholder);
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end loop;
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New_Line;
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Put_Line ("Number of primes up to " & Last'Image &" =" & Count'Image);
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for N in Last + 1 .. 100_000 loop
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Tot := Totient (N);
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if Tot = N - 1 then
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Count := Count + 1;
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end if;
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if N = 100 or N = 1_000 or N mod 10_000 = 0 then
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Put_Line ("Number of primes up to " & N'Image & " =" & Count'Image);
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end if;
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end loop;
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end Totient;
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@ -1,7 +1,7 @@
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scope # Totient function
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# returns the number of integers k where 1 <= k <= n that are mutually prime to n
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local procedure totient( n :: number ) :: number
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local proc totient( n :: number ) :: number
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if n < 3 then result := 1
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elif n = 3 then result := 2
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else
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@ -18,7 +18,7 @@ loop 1..100000 'i [
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t: totient i
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prime?: 1 = i - t
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if i < 26 [
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prints ~« Φ(|pad.with:`0` to :string i 2|) = |pad to :string t 2|
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prints ~« Φ(|pad.with:'0' to :string i 2|) = |pad to :string t 2|
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if prime? -> prints ", prime"
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print ""
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]
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@ -1,93 +0,0 @@
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IDENTIFICATION DIVISION.
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PROGRAM-ID. TOTIENT-FUNCTION.
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DATA DIVISION.
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WORKING-STORAGE SECTION.
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01 TOTIENT-CALCULATION.
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03 N PIC 9(6).
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03 TOTIENT PIC 9(6).
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03 DIVISOR PIC 9(6).
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03 DIV-SQUARE PIC 9(6).
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03 MODULUS PIC 9(6).
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01 LOOP-VARS.
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03 PRIME-COUNT PIC 9(4).
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03 CURRENT-N PIC 9(6).
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03 PRIME-TOTIENT PIC 9(6).
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01 OUTPUTFORMAT.
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03 HEADER PIC X(20) VALUE " N Totient Prime?".
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03 TOTIENT-ROW.
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05 OUT-N PIC Z9.
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05 FILLER PIC XX VALUE SPACES.
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05 OUT-TOTIENT PIC Z(6)9.
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05 FILLER PIC XX VALUE SPACES.
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05 OUT-PRIME PIC X(5).
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03 PRIME-COUNT-ROW.
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05 FILLER PIC X(22) VALUE "Number of primes up to".
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05 OUT-PRMTO PIC Z(5)9.
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05 FILLER PIC XX VALUE ": ".
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05 OUT-PRMCNT PIC ZZZ9.
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PROCEDURE DIVISION.
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BEGIN.
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MOVE ZERO TO PRIME-COUNT.
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DISPLAY HEADER.
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PERFORM SHOW-SMALL-TOTIENT
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VARYING CURRENT-N FROM 1 BY 1
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UNTIL CURRENT-N IS GREATER THAN 25.
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MOVE 25 TO OUT-PRMTO.
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MOVE PRIME-COUNT TO OUT-PRMCNT.
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DISPLAY PRIME-COUNT-ROW.
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PERFORM COUNT-PRIMES
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VARYING CURRENT-N FROM 26 BY 1
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UNTIL CURRENT-N IS GREATER THAN 10000.
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STOP RUN.
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SHOW-SMALL-TOTIENT.
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MOVE CURRENT-N TO N.
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PERFORM CALCULATE-TOTIENT.
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MOVE CURRENT-N TO OUT-N.
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MOVE TOTIENT TO OUT-TOTIENT.
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MOVE "No" TO OUT-PRIME.
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SUBTRACT 1 FROM CURRENT-N GIVING PRIME-TOTIENT.
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IF TOTIENT IS EQUAL TO PRIME-TOTIENT,
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MOVE "Yes" TO OUT-PRIME,
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ADD 1 TO PRIME-COUNT.
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DISPLAY TOTIENT-ROW.
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COUNT-PRIMES.
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MOVE CURRENT-N TO N.
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PERFORM CALCULATE-TOTIENT.
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SUBTRACT 1 FROM CURRENT-N GIVING PRIME-TOTIENT.
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IF TOTIENT IS EQUAL TO PRIME-TOTIENT, ADD 1 TO PRIME-COUNT.
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IF CURRENT-N IS EQUAL TO 100 OR 1000 OR 10000,
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MOVE CURRENT-N TO OUT-PRMTO,
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MOVE PRIME-COUNT TO OUT-PRMCNT,
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DISPLAY PRIME-COUNT-ROW.
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CALCULATE-TOTIENT.
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MOVE N TO TOTIENT.
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MOVE 2 TO DIVISOR.
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MOVE 4 TO DIV-SQUARE.
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PERFORM DIVIDE-STEP.
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PERFORM DIVIDE-STEP
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VARYING DIVISOR FROM 3 BY 2
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UNTIL DIV-SQUARE IS GREATER THAN N.
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IF N IS GREATER THAN 1,
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COMPUTE TOTIENT = TOTIENT - TOTIENT / N.
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DIVIDE-STEP.
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MULTIPLY DIVISOR BY DIVISOR GIVING DIV-SQUARE.
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DIVIDE N BY DIVISOR GIVING MODULUS.
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MULTIPLY DIVISOR BY MODULUS.
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SUBTRACT MODULUS FROM N GIVING MODULUS.
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IF MODULUS IS ZERO,
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PERFORM DIVIDE-OUT UNTIL MODULUS IS NOT ZERO,
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COMPUTE TOTIENT = TOTIENT - TOTIENT / DIVISOR.
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DIVIDE-OUT.
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DIVIDE DIVISOR INTO N.
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DIVIDE N BY DIVISOR GIVING MODULUS.
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MULTIPLY DIVISOR BY MODULUS.
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SUBTRACT MODULUS FROM N GIVING MODULUS.
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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 'TOTIENT FUNCTION (PHI)'
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say version
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@ -92,8 +92,4 @@ end
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say
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return
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include Functions
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include Special
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include Numbers
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include Sequences
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include Abend
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include Math
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