Category:PrimTrial

unit primTrial

Works with: Free Pascal
Works with: Delphi

Maybe NativeUint must be typed in older versions to LongWord aka cardinal

<lang pascal>unit primTrial; // NativeUInt: LongWord 32-Bit-OS/ Uint64 64-Bit-OS {$IFDEF FPC}

 {$MODE DELPHI}
 {$Smartlink ON}
 {$OPTIMIZATION ON,Regvar,PEEPHOLE,CSE,ASMCSE}
 {$CODEALIGN proc=32}

{$ENDIF}

interface type

 ptPrimeList = array of NativeUint;
 procedure InitPrime;
 function actPrime :NativeUint;
 function isPrime(pr: NativeUint):boolean;
 function isAlmostPrime(n: NativeUint;cnt: NativeUint): boolean;
 function isSemiprime(n: NativeUint): boolean;
 function SmallFactor(pr: NativeUint):NativeUint;
 //next prime
 function NextPrime: NativeUint;
 //next possible prime of number wheel
 function NextPosPrim: NativeUint;
 //next prime greater equal limit
 function PrimeGELimit(Limit:NativeUint):NativeUint;
 function PrimeRange(LowLmt,UpLmt:NativeUint): ptPrimeList;

implementation

uses

 sysutils;

const

 cntsmallPrimes = 6;
 smallPrimes : array[0..cntsmallPrimes-1] of NativeUint = (2,3,5,7,11,13);
 wheelSize = (2-1)*(3-1)*(5-1)*(7-1)*(11-1)*(13-1);
 wheelCircumfence = 2*3*5*7*11*13;

var

 deltaWheel : array[0..wheelSize-1] of byte;
 WheelIdx : nativeUint;
 p,pw  : nativeUint;

procedure InitPrime; //initialies wheel and prime to startposition Begin

 p := 2;
 pw := 1;
 WheelIdx := 0;

end;

function actPrime :NativeUint; Begin

 result := p;

end;

procedure InitWheel; //search for numbers that are no multiples of smallprimes //saving only the distance, to keep size small var

 p0,p1,i,d,res : NativeUint;

Begin

 p0 := 1;d := 0;p1 := p0;
 repeat
   Repeat
     p1 := p1+2;// only odd
     i := 1;
     repeat
       res := p1 mod smallPrimes[i];
       inc(i)
     until (res =0)OR(i >= cntSmallPrimes);
     if res <> 0 then
     Begin
       deltaWheel[d] := p1-p0;
       inc(d);
       break;
     end;
   until false;
   p0 := p1;
 until d >= wheelSize;

end;

function biggerFactor(p: NativeUint):NativeUint; //trial division by wheel numbers //reduces count of divisions from 1/2 = 0.5( only odd numbers ) //to 5760/30030 = 0.1918 var

 sp : NativeUint;
 d  : NativeUint;
 r  : NativeUint;

Begin

 sp := 1;d := 0;
 repeat
   sp := sp+deltaWheel[d];
   r := p mod sp;
   d := d+1;
   //IF d = WheelSize then d := 0;
   d := d AND NativeUint(-ord(d<>WheelSize));
   IF r = 0 then
     BREAK;
 until p < sp*sp;
 IF r = 0  then
   result := sp
 else
   result := p;

end;

function SmallFactor(pr: NativeUint):NativeUint; //checking numbers omitted by biggerFactor var

 k : NativeUint;

Begin

 result := pr;
 IF pr in [2,3,5,7,11,13] then
   EXIT;
 IF NOT(ODD(pr))then Begin result := 2; EXIT end;
 For k := 1 to cntSmallPrimes-1 do
 Begin
   IF pr Mod smallPrimes[k] = 0 then
   Begin
     result := smallPrimes[k];
     EXIT
   end;
 end;
 k  := smallPrimes[cntsmallPrimes-1];
 IF pr>k*k then
   result := biggerFactor(pr);

end;

function isPrime(pr: NativeUint):boolean; Begin

 IF pr > 1 then
   isPrime := smallFactor(pr) = pr
 else
   isPrime := false;

end;

function isAlmostPrime(n: NativeUint;cnt: NativeUint): boolean; var

 fac1,c : NativeUint;

begin

 c := 0;
 repeat
   fac1 := SmallFactor(n);
   n := n div fac1;
   inc(c);
 until (n = 1) OR (c > cnt);
 isAlmostPrime := (n = 1) AND (c = cnt);

end;

function isSemiprime(n: NativeUint): boolean; begin

 result := isAlmostPrime(n,2);

end;

function NextPosPrim: NativeUint; var

 WI : NativeUint;

Begin

 result := pw+deltaWheel[WheelIdx];
 WI := (WheelIdx+1);
 WheelIdx := WI AND NativeUint(-ORD(WI<>WheelSize));
 pw := result;

end;

function NextPrime: NativeUint; Begin

 IF p >= smallPrimes[High(smallPrimes)]then
 Begin
   repeat
   until isPrime(NextPosPrim);
   result := pw;
   p := result;
 end
 else
 Begin
   result := 0;
   while p >= smallPrimes[result] do
     inc(result);
   result := smallPrimes[result];
   p:= result;
 end;

end;

function PrimeGELimit(Limit:NativeUint):NativeUint; //prime greater or equal limit Begin

 IF Limit > wheelCircumfence then
 Begin
   WheelIdx:= wheelSize-1;
   result := (Limit DIV wheelCircumfence)*wheelCircumfence-1;
   pw := result;
   //the easy way, no prime test
   while pw <= Limit do
     NextPosPrim;
   result := pw;
   p := result;
   if Not(isPrime(result)) then
     result := NextPrime;
 end
 else
 Begin
   InitPrime;
   repeat
   until (NextPosPrim >= limit) AND isPrime(pw);
   result := pw;
   p := result;
 end;

end;

function PrimeRange(LowLmt,UpLmt:NativeUint): ptPrimeList; var

 i,newP : NativeUint;

Begin

 IF LowLmt>UpLmt then
 Begin
   setlength(result,0);
   EXIT;
 end;
 i := 0;
 setlength(result,100);
 newP := PrimeGELimit(LowLmt);
 while newP<= UpLmt do
 Begin
   result[i]:= newP;
   inc(i);
   IF  i>High(result) then
     setlength(result,i*2);
   newP := NextPrime;
 end;
 setlength(result,i);

end;

//initialization Begin

 InitWheel;
 InitPrime;

end. </lang>