Data commit

Task/Totient-function/Pascal/totient-function-1.pas

@@ -0,0 +1,65 @@
+{$IFDEF FPC}
+  {$MODE DELPHI}
+{$IFEND}
+function gcd_mod(u, v: NativeUint): NativeUint;inline;
+//prerequisites  u > v and u,v > 0
+  var
+    t: NativeUInt;
+  begin
+    repeat
+      t := u;
+      u := v;
+      v := t mod v;
+    until v = 0;
+    gcd_mod := u;
+  end;
+
+function Totient(n:NativeUint):NativeUint;
+var
+  i : NativeUint;
+Begin
+  result := 1;
+  For i := 2 to n do
+    inc(result,ORD(GCD_mod(n,i)=1));
+end;
+
+function CheckPrimeTotient(n:NativeUint):Boolean;inline;
+begin
+  result :=  (Totient(n) = (n-1));
+end;
+
+procedure OutCountPrimes(n:NativeUInt);
+var
+  i,cnt :  NativeUint;
+begin
+  cnt := 0;
+  For i := 1 to n do
+    inc(cnt,Ord(CheckPrimeTotient(i)));
+  writeln(n:10,cnt:8);
+end;
+
+procedure display(n:NativeUint);
+var
+  idx,phi : NativeUint;
+Begin
+  if n = 0 then
+    EXIT;
+  writeln('number n':5,'Totient(n)':11,'isprime':8);
+  For idx := 1 to n do
+  Begin
+    phi := Totient(idx);
+    writeln(idx:4,phi:10,(phi=(idx-1)):12);
+  end
+end;
+var
+  i : NativeUint;
+Begin
+  display(25);
+
+  writeln('Limit  primecount');
+  i := 100;
+  repeat
+    OutCountPrimes(i);
+    i := i*10;
+  until i >100000;
+end.

Task/Totient-function/Pascal/totient-function-2.pas

@@ -0,0 +1,68 @@
+function totient(n:NativeUInt):NativeUInt;
+const
+  //delta of numbers not divisible by 2,3,5 (0_1+6->7+4->11 ..+6->29+2->3_1
+  delta : array[0..7] of NativeUint = (6,4,2,4,2,4,6,2);
+var
+  i, quot,idx: NativeUint;
+Begin
+  // div mod by constant is fast.
+  //i = 2
+  result := n;
+  if (2*2 <= n) then
+  Begin
+    IF not(ODD(n)) then
+    Begin
+      // remove numbers with factor 2,4,8,16, ...
+      while not(ODD(n)) do
+        n := n DIV 2;
+      //remove count of multiples of 2
+      dec(result,result DIV 2);
+    end;
+  end;
+  //i = 3
+  If (3*3 <= n) AND (n mod 3 = 0) then
+  Begin
+    repeat
+      quot := n DIV 3;
+      IF n <> quot*3 then
+        BREAK
+      else
+        n := quot;
+    until false;
+    dec(result,result DIV 3);
+  end;
+  //i = 5
+  If (5*5 <= n) AND (n mod 5 = 0) then
+  Begin
+    repeat
+      quot := n DIV 5;
+      IF n <> quot*5 then
+        BREAK
+      else
+        n := quot;
+    until false;
+    dec(result,result DIV 5);
+  end;
+  i := 7;
+  idx := 1;
+  //i = 7,11,13,17,19,23,29, ...49 ..
+  while i*i <= n do
+  Begin
+    quot := n DIV i;
+    if n = quot*i then
+    Begin
+      repeat
+        IF n <> quot*i then
+          BREAK
+        else
+          n := quot;
+        quot := n DIV i;
+      until false;
+      dec(result,result DIV i);
+    end;
+    i := i + delta[idx];
+    idx := (idx+1) AND 7;
+  end;
+  if n> 1 then
+    dec(result,result div n);
+end;