Removed unused dividers factorization
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33e7b64276
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@ -34,52 +34,6 @@ type
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class function LeastCommonMultiple(AValue1, AValue2: Int64): Int64;
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end;
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TInt64Array = array of Int64;
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{ TIntegerFactor }
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TIntegerFactor = record
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Factor: Int64;
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Exponent: Byte;
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end;
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TIntegerFactors = specialize TList<TIntegerFactor>;
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{ TIntegerFactorization }
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TIntegerFactorization = class
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public
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class function PollardsRhoAlgorithm(const AValue: Int64): TInt64Array;
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class function GetNormalized(constref AIntegerFactorArray: TInt64Array): TIntegerFactors;
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end;
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{ TDividersEnumerator }
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TDividersEnumerator = class
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private
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FFactors: TIntegerFactors;
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FCurrentExponents: array of Byte;
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function GetCount: Integer;
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public
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constructor Create(constref AIntegerFactorArray: TInt64Array);
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destructor Destroy; override;
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function GetCurrent: Int64;
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function MoveNext: Boolean;
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procedure Reset;
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property Current: Int64 read GetCurrent;
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property Count: Integer read GetCount;
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end;
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{ TDividers }
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TDividers = class
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private
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FFactorArray: TInt64Array;
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public
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constructor Create(constref AIntegerFactorArray: TInt64Array);
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function GetEnumerator: TDividersEnumerator;
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end;
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implementation
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{ TNumberTheory }
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@ -104,177 +58,5 @@ begin
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Result := (Abs(AValue1) div GreatestCommonDivisor(AValue1, AValue2)) * Abs(AValue2);
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end;
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{ TIntegerFactorization }
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// https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm
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class function TIntegerFactorization.PollardsRhoAlgorithm(const AValue: Int64): TInt64Array;
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var
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primes: specialize TList<Int64>;
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composites: specialize TStack<Int64>;
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factor, n: Int64;
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i: Integer;
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function G(const AX, AC: Int64): Int64;
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begin
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Result := (AX * AX + AC) mod n;
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end;
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function FindFactor(const AStartValue, AC: Int64): Int64;
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var
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x, y, d: Int64;
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begin
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x := AStartValue;
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y := x;
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d := 1;
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while d = 1 do
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begin
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x := G(x, AC);
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y := G(G(y, AC), AC);
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d := TNumberTheory.GreatestCommonDivisor(Abs(x - y), n);
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end;
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Result := d;
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end;
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begin
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primes := specialize TList<Int64>.Create;
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composites := specialize TStack<Int64>.Create;
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n := Abs(AValue);
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while (n and 1) = 0 do
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begin
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primes.Add(2);
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n := n shr 1;
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end;
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composites.Push(n);
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while composites.Count > 0 do
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begin
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n := composites.Pop;
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i := 0;
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repeat
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factor := FindFactor(2 + (i + 1) div 2, 1 - i div 2);
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if factor < n then
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begin
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composites.Push(factor);
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composites.Push(n div factor);
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end;
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Inc(i);
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until (factor < n) or (i > 3);
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if factor = n then
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primes.Add(factor);
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end;
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Result := primes.ToArray;
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primes.Free;
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composites.Free;
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end;
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class function TIntegerFactorization.GetNormalized(constref AIntegerFactorArray: TInt64Array): TIntegerFactors;
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var
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i: Integer;
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factor: Int64;
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normal: TIntegerFactor;
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found: Boolean;
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begin
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Result := TIntegerFactors.Create;
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for factor in AIntegerFactorArray do
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begin
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found := False;
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for i := 0 to Result.Count - 1 do
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if Result[i].Factor = factor then
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begin
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found := True;
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normal := Result[i];
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Inc(normal.Exponent);
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Result[i] := normal;
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Break;
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end;
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if not found then
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begin
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normal.Factor := factor;
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normal.Exponent := 1;
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Result.Add(normal);
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end;
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end;
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end;
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{ TDividersEnumerator }
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function TDividersEnumerator.GetCount: Integer;
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var
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factor: TIntegerFactor;
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begin
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if FFactors.Count > 0 then
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begin
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Result := 1;
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for factor in FFactors do
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Result := Result * factor.Exponent;
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Dec(Result);
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end
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else
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Result := 0;
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end;
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constructor TDividersEnumerator.Create(constref AIntegerFactorArray: TInt64Array);
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begin
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FFactors := TIntegerFactorization.GetNormalized(AIntegerFactorArray);
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SetLength(FCurrentExponents, FFactors.Count);
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end;
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destructor TDividersEnumerator.Destroy;
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begin
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FFactors.Free;
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end;
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function TDividersEnumerator.GetCurrent: Int64;
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var
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i: Integer;
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begin
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Result := 1;
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for i := Low(FCurrentExponents) to High(FCurrentExponents) do
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if FCurrentExponents[i] > 0 then
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Result := Result * Round(Power(FFactors[i].Factor, FCurrentExponents[i]));
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end;
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function TDividersEnumerator.MoveNext: Boolean;
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var
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i: Integer;
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begin
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Result := False;
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i := 0;
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while (i <= High(FCurrentExponents)) and (FCurrentExponents[i] >= FFactors[i].Exponent) do
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begin
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FCurrentExponents[i] := 0;
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Inc(i);
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end;
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if i <= High(FCurrentExponents) then
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begin
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Inc(FCurrentExponents[i]);
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Result := True;
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end;
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end;
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procedure TDividersEnumerator.Reset;
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var
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i: Integer;
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begin
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for i := Low(FCurrentExponents) to High(FCurrentExponents) do
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FCurrentExponents[i] := 0;
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end;
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{ TDividers }
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constructor TDividers.Create(constref AIntegerFactorArray: TInt64Array);
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begin
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FFactorArray := AIntegerFactorArray;
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end;
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function TDividers.GetEnumerator: TDividersEnumerator;
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begin
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Result := TDividersEnumerator.Create(FFactorArray);
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end;
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end.
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