Data update

Task/Totient-function/BASIC/totient-function.basic

@@ -0,0 +1,27 @@
+10 DEFINT A-Z: DIM B$(2): B$(0)="No": B$(1)="Yes"
+20 PRINT " N  Totient  Prime"
+30 FOR N=1 TO 25
+40 GOSUB 200
+50 P=-(T=N-1)
+60 C=C+P
+70 PRINT USING "##  #######  \   \";N;T;B$(P)
+80 NEXT N
+90 F$="Number of primes up to ######: ####"
+100 PRINT USING F$;25;C
+110 FOR N=26 TO 10000
+120 GOSUB 200
+130 C=C-(T=N-1)
+140 IF N=100 OR N=1000 OR N=10000 THEN PRINT USING F$;N;C
+150 NEXT N
+160 END
+200 REM T = TOTIENT(N)
+210 T=N: Z=N
+220 I=2: GOSUB 270
+230 I=3
+240 IF I*I<=Z THEN GOSUB 270: I=I+2: GOTO 240
+250 IF Z>1 THEN T=T-T\Z
+260 RETURN
+270 IF Z MOD I<>0 THEN RETURN
+280 IF Z MOD I=0 THEN Z = Z\I: GOTO 280
+290 T = T-T\I
+300 RETURN

Task/Totient-function/BCPL/totient-function.bcpl

@@ -0,0 +1,31 @@
+get "libhdr"
+
+let totient(n) = valof
+$(  let tot = n and i = 2
+    while i*i <= n
+    $(  if n rem i = 0
+        $(  while n rem i = 0 do n := n / i
+            tot := tot - tot/i
+        $)
+        if i=2 then i:=1
+        i := i+2
+    $)
+    resultis n>1 -> tot-tot/n, tot
+$)
+
+let start() be
+$(  let count = 0
+    writes(" N  Totient  Prime*N")
+    for n = 1 to 25
+    $(  let tot = totient(n)
+        let prime = n-1 = tot
+        if prime then count := count + 1
+        writef("%I2  %I7  %S*N", n, tot, prime -> "  Yes", "   No")
+    $)
+    writef("Number of primes up to %I6: %I4*N", 25, count)
+    for n = 26 to 10000
+    $(  if totient(n) = n-1 then count := count + 1
+        if n = 100 | n = 1000 | n = 10000 then
+            writef("Number of primes up to %I6: %I4*N", n, count)
+    $)
+$)

Task/Totient-function/CLU/totient-function.clu

@@ -0,0 +1,50 @@
+totient = proc (n: int) returns (int)
+    tot: int := n
+
+    i: int := 2
+    while i*i <= n do
+        if n//i = 0 then
+            while n//i = 0 do
+                n := n/i
+            end
+            tot := tot-tot/i
+        end
+        if i=2 then i:=1 end
+        i := i+2
+    end
+    if n>1 then
+        tot := tot-tot/n
+    end
+    return(tot)
+end totient
+
+start_up = proc ()
+    po: stream := stream$primary_output()
+    count: int := 0
+
+    stream$putl(po, " N  Totient  Prime")
+    for n: int in int$from_to(1, 25) do
+        tot: int := totient(n)
+        stream$putright(po, int$unparse(n), 2)
+        stream$putright(po, int$unparse(tot), 9)
+        if n-1 = tot then
+            stream$putright(po, "Yes", 7)
+            count := count + 1
+        else
+            stream$putright(po, "No", 7)
+        end
+        stream$putl(po, "")
+    end
+
+    stream$putl(po, "Number of primes up to 25:\t" || int$unparse(count))
+    for n: int in int$from_to(26, 100000) do
+        if totient(n) = n-1 then
+            count := count + 1
+        end
+        if n = 100 cor n = 1000 cor n // 10000 = 0 then
+            stream$putl(po, "Number of primes up to "
+                        || int$unparse(n) || ":\t"
+                        || int$unparse(count))
+        end
+    end
+end start_up

Task/Totient-function/COBOL/totient-function.cobol

@@ -0,0 +1,93 @@
+       IDENTIFICATION DIVISION.
+       PROGRAM-ID. TOTIENT-FUNCTION.
+
+       DATA DIVISION.
+       WORKING-STORAGE SECTION.
+       01 TOTIENT-CALCULATION.
+          03 N               PIC 9(6).
+          03 TOTIENT         PIC 9(6).
+          03 DIVISOR         PIC 9(6).
+          03 DIV-SQUARE      PIC 9(6).
+          03 MODULUS         PIC 9(6).
+
+       01 LOOP-VARS.
+          03 PRIME-COUNT     PIC 9(4).
+          03 CURRENT-N       PIC 9(6).
+          03 PRIME-TOTIENT   PIC 9(6).
+
+       01 OUTPUTFORMAT.
+          03 HEADER          PIC X(20) VALUE " N  Totient  Prime?".
+          03 TOTIENT-ROW.
+             05 OUT-N        PIC Z9.
+             05 FILLER       PIC XX VALUE SPACES.
+             05 OUT-TOTIENT  PIC Z(6)9.
+             05 FILLER       PIC XX VALUE SPACES.
+             05 OUT-PRIME    PIC X(5).
+          03 PRIME-COUNT-ROW.
+             05 FILLER       PIC X(22) VALUE "Number of primes up to".
+             05 OUT-PRMTO    PIC Z(5)9.
+             05 FILLER       PIC XX VALUE ": ".
+             05 OUT-PRMCNT   PIC ZZZ9.
+
+       PROCEDURE DIVISION.
+       BEGIN.
+           MOVE ZERO TO PRIME-COUNT.
+           DISPLAY HEADER.
+           PERFORM SHOW-SMALL-TOTIENT
+               VARYING CURRENT-N FROM 1 BY 1
+               UNTIL CURRENT-N IS GREATER THAN 25.
+           MOVE 25 TO OUT-PRMTO.
+           MOVE PRIME-COUNT TO OUT-PRMCNT.
+           DISPLAY PRIME-COUNT-ROW.
+           PERFORM COUNT-PRIMES
+               VARYING CURRENT-N FROM 26 BY 1
+               UNTIL CURRENT-N IS GREATER THAN 10000.
+           STOP RUN.
+
+       SHOW-SMALL-TOTIENT.
+           MOVE CURRENT-N TO N.
+           PERFORM CALCULATE-TOTIENT.
+           MOVE CURRENT-N TO OUT-N.
+           MOVE TOTIENT TO OUT-TOTIENT.
+           MOVE "No" TO OUT-PRIME.
+           SUBTRACT 1 FROM CURRENT-N GIVING PRIME-TOTIENT.
+           IF TOTIENT IS EQUAL TO PRIME-TOTIENT,
+               MOVE "Yes" TO OUT-PRIME,
+               ADD 1 TO PRIME-COUNT.
+           DISPLAY TOTIENT-ROW.
+
+       COUNT-PRIMES.
+           MOVE CURRENT-N TO N.
+           PERFORM CALCULATE-TOTIENT.
+           SUBTRACT 1 FROM CURRENT-N GIVING PRIME-TOTIENT.
+           IF TOTIENT IS EQUAL TO PRIME-TOTIENT, ADD 1 TO PRIME-COUNT.
+           IF CURRENT-N IS EQUAL TO 100 OR 1000 OR 10000,
+               MOVE CURRENT-N TO OUT-PRMTO,
+               MOVE PRIME-COUNT TO OUT-PRMCNT,
+               DISPLAY PRIME-COUNT-ROW.
+
+       CALCULATE-TOTIENT.
+           MOVE N TO TOTIENT.
+           MOVE 2 TO DIVISOR.
+           MOVE 4 TO DIV-SQUARE.
+           PERFORM DIVIDE-STEP.
+           PERFORM DIVIDE-STEP
+               VARYING DIVISOR FROM 3 BY 2
+               UNTIL DIV-SQUARE IS GREATER THAN N.
+           IF N IS GREATER THAN 1,
+               COMPUTE TOTIENT = TOTIENT - TOTIENT / N.
+
+       DIVIDE-STEP.
+           MULTIPLY DIVISOR BY DIVISOR GIVING DIV-SQUARE.
+           DIVIDE N BY DIVISOR GIVING MODULUS.
+           MULTIPLY DIVISOR BY MODULUS.
+           SUBTRACT MODULUS FROM N GIVING MODULUS.
+           IF MODULUS IS ZERO,
+               PERFORM DIVIDE-OUT UNTIL MODULUS IS NOT ZERO,
+               COMPUTE TOTIENT = TOTIENT - TOTIENT / DIVISOR.
+
+       DIVIDE-OUT.
+           DIVIDE DIVISOR INTO N.
+           DIVIDE N BY DIVISOR GIVING MODULUS.
+           MULTIPLY DIVISOR BY MODULUS.
+           SUBTRACT MODULUS FROM N GIVING MODULUS.

Task/Totient-function/Cowgol/totient-function.cowgol

@@ -0,0 +1,61 @@
+include "cowgol.coh";
+
+sub totient(n: uint32): (tot: uint32) is
+    tot := n;
+
+    var i: uint32 := 2;
+    while i*i <= n loop
+        if n%i == 0 then
+            while n%i == 0 loop
+                n := n/i;
+            end loop;
+            tot := tot - tot/i;
+        end if;
+        if i == 2 then
+            i := 1;
+        end if;
+        i := i + 2;
+    end loop;
+
+    if n > 1 then
+        tot := tot - tot/n;
+    end if;
+end sub;
+
+var count: uint16 := 0;
+
+print("N\tTotient\tPrime\n");
+var n: uint32 := 1;
+while n <= 25 loop
+    var tot := totient(n);
+    print_i32(n);
+    print_char('\t');
+    print_i32(tot);
+    print_char('\t');
+    if n-1 == tot then
+        count := count + 1;
+        print("Yes\n");
+    else
+        print("No\n");
+    end if;
+    n := n + 1;
+end loop;
+
+print("Number of primes up to 25:\t");
+print_i16(count);
+print_nl();
+
+while n <= 100000 loop
+    tot := totient(n);
+    if n-1 == tot then
+        count := count + 1;
+    end if;
+    if n == 100 or n == 1000 or n % 10000 == 0 then
+        print("Number of primes up to ");
+        print_i32(n);
+        print(":\t");
+        print_i16(count);
+        print_nl();
+    end if;
+    n := n + 1;
+end loop;

Task/Totient-function/Draco/totient-function.draco

@@ -0,0 +1,39 @@
+proc totient(word n) word:
+    word tot, i;
+    tot := n;
+    i := 2;
+    while i*i <= n do
+        if n%i = 0 then
+            while n%i = 0 do n := n/i od;
+            tot := tot - tot/i
+        fi;
+        if i=2 then i:=1 fi;
+        i := i+2
+    od;
+    if n>1 then
+        tot - tot/n
+    else
+        tot
+    fi
+corp
+
+proc main() void:
+    word count, n, tot;
+    bool prime;
+
+    count := 0;
+    writeln(" N  Totient  Prime");
+    for n from 1 upto 25 do
+        tot := totient(n);
+        prime := n-1 = tot;
+        if prime then count := count+1 fi;
+        writeln(n:2, "  ", tot:7, "  ", if prime then "  Yes" else "   No" fi)
+    od;
+    writeln("Number of primes up to ",25:6,": ",count:4);
+    for n from 25 upto 10000 do
+        if totient(n) = n-1 then count := count+1 fi;
+        if n=100 or n=1000 or n=10000 then
+            writeln("Number of primes up to ",n:6,": ",count:4)
+        fi
+    od
+corp

Task/Totient-function/MAD/totient-function.mad

@@ -0,0 +1,45 @@
+            NORMAL MODE IS INTEGER
+            BOOLEAN PRM
+
+            INTERNAL FUNCTION(A,B)
+            ENTRY TO REM.
+            FUNCTION RETURN A-A/B*B
+            END OF FUNCTION
+
+            INTERNAL FUNCTION(NN)
+            ENTRY TO TOTENT.
+            N = NN
+            TOT = N
+            THROUGH STEP, FOR I=2, 2, I*I.G.N
+            WHENEVER REM.(N,I).E.0
+                THROUGH DIV, FOR N=N, 0, REM.(N,I).NE.0
+DIV             N = N/I
+                TOT = TOT-TOT/I
+            END OF CONDITIONAL
+            WHENEVER I.E.2, I=1
+STEP        CONTINUE
+            WHENEVER N.G.1, TOT = TOT-TOT/N
+            FUNCTION RETURN TOT
+            END OF FUNCTION
+
+            COUNT = 0
+            PRINT FORMAT HEADER
+            THROUGH FRST25, FOR KN=1, 1, KN.G.25
+            KTOT = TOTENT.(KN)
+            PRM = KTOT.E.KN-1
+            WHENEVER PRM, COUNT = COUNT + 1
+FRST25      PRINT FORMAT NUMTOT,KN,KTOT,PRM
+
+            PRINT FORMAT NUMPRM,25,COUNT
+
+            THROUGH CNTPRM, FOR KN=26, 1, KN.G.100000
+            KTOT = TOTENT.(KN)
+            WHENEVER KTOT.E.KN-1, COUNT = COUNT+1
+            WHENEVER KN.E.100 .OR. KN.E.1000 .OR. REM.(KN,10000).E.0,
+          0     PRINT FORMAT NUMPRM,KN,COUNT
+CNTPRM      CONTINUE
+
+            VECTOR VALUES HEADER = $19H  N  TOTIENT  PRIME*$
+            VECTOR VALUES NUMTOT = $I2,S2,I7,S2,I5*$
+            VECTOR VALUES NUMPRM = $22HNUMBER OF PRIMES UP TO,I7,1H:,I6*$
+            END OF PROGRAM

Task/Totient-function/Miranda/totient-function.miranda

@@ -0,0 +1,25 @@
+main :: [sys_message]
+main = [Stdout (lay (map showline [1..25])),
+        Stdout (lay (map countprimes (25:map (10^) [2..5])))]
+
+countprimes :: num->[char]
+countprimes n = "There are " ++ show amount ++ " primes up to " ++ show n
+                where amount = #filter prime [2..n]
+
+showline :: num->[char]
+showline n = "phi(" ++ show n ++ ") = " ++ show (totient n) ++ ", " ++ kind
+             where kind = "prime", if prime n
+                        = "composite", otherwise
+
+prime :: num->bool
+prime n = totient n = n - 1
+
+totient :: num->num
+totient n = loop n n (2:[3, 5..])
+            where loop tot n (d:ds)
+                   = tot, if n<=1
+                   = tot - tot div n, if d*d > n
+                   = loop tot n ds, if n mod d ~= 0
+                   = loop (tot - tot div d) (remfac n d) ds, otherwise
+                  remfac n d = n, if n mod d ~= 0
+                             = remfac (n div d) d, otherwise

Task/Totient-function/Modula-2/totient-function.mod2

@@ -0,0 +1,62 @@
+MODULE TotientFunction;
+FROM InOut IMPORT WriteString, WriteCard, WriteLn;
+
+VAR count, n, tot: CARDINAL;
+
+PROCEDURE totient(n: CARDINAL): CARDINAL;
+    VAR tot, i: CARDINAL;
+BEGIN
+    tot := n;
+    i := 2;
+    WHILE i*i <= n DO
+        IF n MOD i = 0 THEN
+            WHILE n MOD i = 0 DO
+                n := n DIV i
+            END;
+            DEC(tot, tot DIV i)
+        END;
+        IF i=2 THEN i := 1 END;
+        INC(i, 2)
+    END;
+    IF n>1 THEN
+        DEC(tot, tot DIV n)
+    END;
+    RETURN tot
+END totient;
+
+PROCEDURE ShowPrimeCount(n, count: CARDINAL);
+BEGIN
+    WriteString("Number of primes up to");
+    WriteCard(n, 6);
+    WriteString(": ");
+    WriteCard(count, 4);
+    WriteLn
+END ShowPrimeCount;
+
+BEGIN
+    count := 0;
+
+    WriteString(" N  Totient  Prime");
+    WriteLn;
+    FOR n := 1 TO 25 DO
+        tot := totient(n);
+        WriteCard(n, 2);
+        WriteCard(tot, 9);
+        IF tot = n-1 THEN
+            WriteString("    Yes");
+            INC(count)
+        ELSE
+            WriteString("     No")
+        END;
+        WriteLn
+    END;
+
+    ShowPrimeCount(25, count);
+
+    FOR n := 26 TO 10000 DO
+        IF totient(n) = n-1 THEN INC(count) END;
+        IF (n=100) OR (n=1000) OR (n=10000) THEN
+            ShowPrimeCount(n, count)
+        END;
+    END
+END TotientFunction.

Task/Totient-function/PL-I/totient-function.pli

@@ -0,0 +1,41 @@
+totientFunction: procedure options(main);
+    totient: procedure(nn) returns(fixed);
+        declare (nn, n, i, tot) fixed;
+        n = nn;
+        tot = n;
+        do i=2 repeat(i+2) while(i*i <= n);
+            if mod(n,i) = 0 then do;
+                do while(mod(n,i) = 0);
+                    n = n / i;
+                end;
+                tot = tot - tot / i;
+            end;
+            if i=2 then i=1;
+        end;
+        if n>1 then tot = tot - tot/n;
+        return(tot);
+    end totient;
+
+    showPrimeCount: procedure(n, primeCount);
+        declare (n, primeCount) fixed;
+        put skip edit('There are', primeCount, ' primes up to', n) (A,F(5),A,F(6));
+    end showPrimeCount;
+
+    declare (n, primeCount, tot) fixed;
+    do n = 1 to 25;
+        tot = totient(n);
+        put edit('phi(', n, ') = ', tot) (A,F(2),A,F(2));
+        if tot = n-1 then do;
+            put list('; prime');
+            primeCount = primeCount + 1;
+        end;
+        put skip;
+    end;
+
+    call showPrimeCount(25, primeCount);
+    do n = 26 to 10000;
+        if totient(n) = n-1 then primeCount = primeCount + 1;
+        if n=100 | n=1000 | n=10000 then
+            call showPrimeCount(n, primeCount);
+    end;
+end totientFunction;

Task/Totient-function/PL-M/totient-function.plm

@@ -0,0 +1,66 @@
+100H:
+BDOS: PROCEDURE (F,A); DECLARE F BYTE, A ADDRESS; GO TO 5; END BDOS;
+EXIT: PROCEDURE; GO TO 0; END EXIT;
+PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9,S); END PRINT;
+
+PRINT$NUM: PROCEDURE (N);
+    DECLARE (N, P) ADDRESS, CH BASED P BYTE;
+    DECLARE S (6) BYTE INITIAL ('.....$');
+    P = .S(5);
+DIGIT:
+    P = P-1;
+    CH = '0' + N MOD 10;
+    IF (N := N/10) > 0 THEN GO TO DIGIT;
+    CALL PRINT(P);
+END PRINT$NUM;
+
+TOTIENT: PROCEDURE (N) ADDRESS;
+    DECLARE (TOT, N, I) ADDRESS;
+    TOT = N;
+    I = 2;
+    DO WHILE I*I <= N;
+        IF N MOD I = 0 THEN DO;
+            DO WHILE (N := N / I) MOD I = 0; END;
+            TOT = TOT - TOT / I;
+        END;
+        IF I=2 THEN I=1;
+        I = I+2;
+    END;
+    IF N > 1 THEN TOT = TOT - TOT / N;
+    RETURN TOT;
+END TOTIENT;
+
+SHOW$PRIME$COUNT: PROCEDURE (N, COUNT);
+    DECLARE (N, COUNT) ADDRESS;
+    CALL PRINT(.'THERE ARE $');
+    CALL PRINT$NUM(COUNT);
+    CALL PRINT(.' PRIMES UP TO $');
+    CALL PRINT$NUM(N);
+    CALL PRINT(.(13,10,'$'));
+END SHOW$PRIME$COUNT;
+
+DECLARE (N, TOT) ADDRESS;
+DECLARE PRIME$COUNT ADDRESS INITIAL (0);
+
+DO N = 1 TO 25;
+    CALL PRINT(.'PHI($');
+    CALL PRINT$NUM(N);
+    CALL PRINT(.') = $');
+    CALL PRINT$NUM(TOT := TOTIENT(N));
+    IF TOT = N-1 THEN DO;
+        CALL PRINT(.'; PRIME$');
+        PRIME$COUNT = PRIME$COUNT + 1;
+    END;
+    CALL PRINT(.(13,10,'$'));
+END;
+
+CALL SHOW$PRIME$COUNT(25, PRIME$COUNT);
+DO N = 26 TO 10000;
+    IF TOTIENT(N) = N-1 THEN
+        PRIME$COUNT = PRIME$COUNT + 1;
+    IF N=100 OR N=1000 OR N=10000 THEN
+        CALL SHOW$PRIME$COUNT(N, PRIME$COUNT);
+END;
+
+CALL EXIT;
+EOF

Task/Totient-function/Ruby/totient-function.rb

@@ -1,7 +1,7 @@
 require "prime"
 
 def 𝜑(n)
-  n.prime_division.inject(1) {|res, (pr, exp)| res *= (pr-1) * pr**(exp-1) }
+  n.prime_division.inject(1){|res, (pr, exp)| res * (pr-1) * pr**(exp-1) }
 end
 
 1.upto 25 do |n|