unit XMLUtils_mX4;      // not finished yet..

interface

{uses
  System.Classes, Winapi.msxml;   }

type
  TStoreFormStruct = record
    Width: Integer;
    Height: Integer;
    Left: Integer;
    Top: Integer;
    Maximized: Boolean;
  end;

function GetArrayIndexByName(const AName: string; const Arr: array of string): Integer;
procedure StringsToXML(AStrings: TStrings; ANode: TXmlNodesimple);   // IDOMNode - TDOMNode
procedure XMLToStrings(AStrings: TStrings; ANode: TXmlNodesimple);
//procedure FormToXML(const AStore: TStoreFormStruct; ANode: TXmlNodesimple);
//procedure XMLToForm(var AStore: TStoreFormStruct; ANode: TXmlNodesimple);
//procedure SaveXMLToFile(const AFileName: string; ADomDoc: TXMLDocument);
procedure AddCDataNodeName(const AName: string);

implementation

//uses
  //SysUtils, JobConsts, Windows;

const
  CDataXMLFormat = '<xsl:output indent="yes" method="xml" encoding="UTF-8" cdata-section-elements="%s"/>';
  XMLFormat = '<?xml version="1.0" encoding="UTF-8"?>' +
              '<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">' +
              '  <xsl:output indent="yes" method="xml" encoding="UTF-8"/> %s ' +
              '    <xsl:template match="/ | @* | node()">' +
              '  <xsl:copy>' +
              '  <xsl:apply-templates select="@* | node()"/>' +
              '    </xsl:copy>' +
              '  </xsl:template>' +
              '</xsl:stylesheet>';
              
 PI1000=             
              
 '3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199';             

var
  CDataNodeNames: TStrings; // = nil;

procedure AddCDataNodeName(const AName: string);
begin
  if (CDataNodeNames = nil) then
  begin
    CDataNodeNames := TStringList.Create();
  end;
  if (CDataNodeNames.IndexOf(AName) < 0) then
  begin
    CDataNodeNames.Add(AName);
  end;
end;

(*              
procedure SaveXMLToFile(const AFileName: string; ADomDoc: IXMLDOMDocument);
  function GetXMLFormat: string;
  var
    i: Integer;
  begin
    Result := '';
    if (CDataNodeNames <> nil) then
    begin
      for i := 0 to CDataNodeNames.Count - 1 do
      begin
        Result := Result + #32 + Format(CDataXMLFormat, [CDataNodeNames[i]]);
      end;
    end;
    Result := Format(XMLFormat, [Result]);
  end;
  
var
  b: Boolean;
  TransDoc, ResDoc: IXMLDOMDocument;
begin
  TransDoc := CoDOMDocument.Create();
  ResDoc := CoDOMDocument.Create();
  TransDoc.loadXML(GetXMLFormat());
  try
    ADomDoc.transformNodeToObject(TransDoc, ResDoc);
    b := (ResDoc.xml <> '');
  except
    b := False;
  end;
  if b then
  begin
    ResDoc.save(AFileName);
  end else
  begin
    ADomDoc.save(AFileName);
  end;
end; *)

function GetArrayIndexByName(const AName: string; const Arr: array of string): Integer;
begin
  for Result := Low(Arr) to High(Arr) do
  begin
    if (CompareText(Arr[Result], AName) = 0) then Exit;
  end;
  Result := -1;
end;

procedure StringsToXML(AStrings: TStrings; ANode: TXmlNodesimple);
var
  ChildNode: TXmlNodesimple; //IXMLDOMNode;
begin
  //ChildNode := ANode.ownerDocument.createCDATASection(AStrings.Text);
  //ANode.appendChild(ChildNode);
end;

procedure XMLToStrings(AStrings: TStrings; ANode: TXmlNodesimple);
begin
  AStrings.Text := ANode.text;
end;

(*
procedure FormToXML(const AStore: TStoreFormStruct; ANode: TXmlNodesimple);
var
  ChildNode: IXMLDOMNode;
begin
  ChildNode := ANode.ownerDocument.createElement('Height');
  ANode.appendChild(ChildNode);
  ChildNode.text := IntToStr(AStore.Height);

  ChildNode := ANode.ownerDocument.createElement('Width');
  ANode.appendChild(ChildNode);
  ChildNode.text := IntToStr(AStore.Width);

  ChildNode := ANode.ownerDocument.createElement('Left');
  ANode.appendChild(ChildNode);
  ChildNode.text := IntToStr(AStore.Left);

  ChildNode := ANode.ownerDocument.createElement('Top');
  ANode.appendChild(ChildNode);
  ChildNode.text := IntToStr(AStore.Top);

  ChildNode := ANode.ownerDocument.createElement('Maximized');
  ANode.appendChild(ChildNode);
  ChildNode.text := cStoreBoolean[AStore.Maximized];
end;  *)

(*
procedure XMLToForm(var AStore: TStoreFormStruct; ANode: IXMLDOMNode);
var
  v: Integer;
  ChildNode: IXMLDOMNode;
begin
  ZeroMemory(@AStore, SizeOf(AStore));

  ChildNode := ANode.selectSingleNode('Height');
  if ChildNode <> nil then
  begin
    AStore.Height := StrToIntDef(ChildNode.text, 0);
  end;

  ChildNode := ANode.selectSingleNode('Width');
  if ChildNode <> nil then
  begin
    AStore.Width := StrToIntDef(ChildNode.text, 0);
  end;

  ChildNode := ANode.selectSingleNode('Left');
  if ChildNode <> nil then
  begin
    AStore.Left := StrToIntDef(ChildNode.text, 0);
  end;

  ChildNode := ANode.selectSingleNode('Top');
  if ChildNode <> nil then
  begin
    AStore.Top := StrToIntDef(ChildNode.text, 0);
  end;

  ChildNode := ANode.selectSingleNode('Maximized');
  if ChildNode <> nil then
  begin
    v := GetArrayIndexByName(ChildNode.text, cStoreBoolean);
    if (v > -1) then AStore.Maximized := Boolean(v);
  end;
end;    *)

function CreateCompactGuidStr2: string;
var
  LIndex: Integer;
  LBytes: TBytes;
  NewGUID: TGUID;
begin
  Result := '';
  //LBytes := TGUID.NewGuid.ToByteArray();
   NewGUID := StringToGUID(CreateClassID);
   //LBytes:= TBytes(GuidtoString(NewGuid));
   //StrToBytes(const Value:Str): TBytes;
    LBytes:= StrToBytes(GuidtoString(NewGuid));
  for LIndex := 0 to Length(LBytes)-1 do
    Result := Result + IntToHex(LBytes[LIndex], 2);
end;


function CreateCompactGuidStr3: string;
var
  LIndex: Integer;
  LBytes: TBytes;
  NewGUID: TGUID;
begin
  Result := '';
  //LBytes := TGUID.NewGuid.ToByteArray();
   NewGUID := deltNewGUID;
   //LBytes:= TBytes(GuidtoString(NewGuid));
   //StrToBytes(const Value:Str): TBytes;
    LBytes:= StrToBytes(GuidtoString(NewGuid));
  for LIndex := 0 to Length(LBytes)-1 do
    Result := Result + IntToHex(LBytes[LIndex], 2);
end;

function CreateCompactGuidStr4: string;
var
  LIndex: Integer;
  LBytes: TBytes;
  NewGUID: TGUID;
begin
  Result := '';
  //LBytes := TGUID.NewGuid.ToByteArray();
   NewGUID := deltNewGUID;
   //LBytes:= TBytes(GuidtoString(NewGuid));
   //StrToBytes(const Value:Str): TBytes;
   result:= GuidtoString(NewGuid);
 
end;

function StreamToBytes2(const ASource: TStream): TBytes;
begin
  SetLength(Result, ASource.Size);
  ASource.Position := 0;
  //if ASource.Read(stringtostream(Result), ASource.Size) <> ASource.Size then
    //raise Exception.Create('Unable to copy all content to TBytes');
   // asource.readbytearray(result, ASource.Size);
      //asource.readAB(result, ASource.Size);
end;

//BytesSetLengthAndZero( var V : TBytes; const NewLength : NativeInt)');

Procedure SetArrayLength2Byte(var arr: TByteArray; asize1: Integer);
var i: Integer;
    ab: array of byte;
begin setlength(arr, asize1);
   //for i:= 0 to asize1-1 do SetLength(arr[i], asize2);
end;

function StreamToBytes3(const ASource: TStream): TBytes; //array of byte; //TByteArray;
var buffstr:String;
begin
  writeln('len '+itoa(asource.size));
  //SetLength(Result, ASource.Size);
  //BytesSetLengthAndZero(Result, ASource.Size);
  //SetArrayLength2Byte(Result, ASource.Size);
  // for it:= 0 to  ASource.Size-1 do result[it]:= 0;
  
  ASource.Position := 0;
  SetLength(buffstr,ASource.Size);
  //for it:= 1 to ASource.Size-1 do buffstr[it]:= '0'; //(ord(buffstr[1])));
  //if ASource.Read(stringtostream(Result), ASource.Size) <> ASource.Size then
    //raise Exception.Create('Unable to copy all content to TBytes');
   // asource.readbytearray(result, ASource.Size);
      //asource.readbytearray(result, ASource.Size);
      asource.read(buffstr, ASource.Size);
    writeln(buffstr)  
    result:= strtobytes(buffstr);
end;

 var Stream: TStringStream;   mybytes: TBytes;

initialization

 AddCDataNodeName('const AName: string');
 writeln(CreateCompactGuidStr2);
 writeln(CreateCompactGuidStr);
 writeln(CreateCompactGuidStr3);
 writeln(CreateCompactGuidStr4);
 
  Stream:= TStringStream.Create('this is my streambox!');
  writeln(Stream.DataString);
 
 //Func StreamToByteArray(Stream: TStream): TBytes;
   writeln(Bytestostr(streamToByteArray(Stream)));
   writeln(Bytestostr(streamToByteArray(Stream)));
    writeln((streamToByte(Stream)));
 //Function StreamToBytes( const ASource : TStream) : TBytes');
   writeln(chr(33))
 
   Stream.Position := 0;
   writeln(Bytestostr(StreamToBytes2(stream)));
     writeln(Bytestostr(GetBytes('value:String thing')));
     writeln('3back: '+Bytestostr(StreamToBytes3(stream)));
      writeln('3len: '+itoa(length(Bytestostr(StreamToBytes3(stream)))));
 
   //writeln(bytestostr(StreamToBytes(stream)));
   
   SetLength(mybytes, 400);
   writeln(itoa(length(mybytes)));
 
  //stream.free;
  
    maxCalcF('SqRT(5)');
    //2.236067977499789696?,
    writeln(Format('%.18f ',[sqrt(5)]));
    
    with TBigfloat.Create1(150) do begin
      assign5(5);
      sqrt;
      writeln(tostring(normal)) ;
      //https://www.wolframalpha.com/input/?i=pi+to+1000+digits
      piconst(1000)
      writeln(tostring(normal)) ;
      writeln('sha test1: '+sha1tohex(synsha1(tostring(normal))));
      writeln('sha test2: '+sha1tohex(synsha1(PI1000)));
      writeln('zero count: '+ itoa(StrCharCount(tostring(normal), '0')));
      for it:= 0 to 9 do 
      writeln(itoa(it)+' count: '+ itoa(StrCount(tostring(normal),+itoa(it)[1])));
      for it:= 0 to 9 do 
        FormatF('%d count: %d',[it,StrCount(toString(normal),+itoa(it)[1])]);
      
      //StrCountChar(const ASource:str;const c:Char;const AStartIdx:Card):Card;
      writeln('3 count: '+ itoa(StrCountChar(tostring(normal), '3',1)));
      free;
    end;  
    
    maXcalcF('((9/10)^30)*100')
  


finalization
  CDataNodeNames.Free();
  writeln(objtostr(stream));
  stream.free;
  //writeln(objtostr(stream));
  stream:= Nil;
  writeln(objtostr(stream));

end.

ref: zero count: 968
0 count: 968
1 count: 1026
2 count: 1022
3 count: 976
4 count: 1012
5 count: 1047
6 count: 1023
7 count: 971
8 count: 948
9 count: 1014
3 count: 976
TStringStream@08987660
nil
 mX4 executed: 07/01/2022 22:48:18  Runtime: 0:0:54.150  Memload: 48% use
PascalScript maXbox4 - RemObjects & SynEdit



function StreamToBytes(const ASource: TStream): TBytes;
begin
  SetLength(Result, ASource.Size);
  ASource.Position := 0;
  if ASource.Read(Result, ASource.Size) <> ASource.Size then
    raise Exception.Create('Unable to copy all content to TBytes');
end;

    Why doesn't Pi have a 0 in its first 30 digits?

For the same reason that e
doesn't have a 6

in its first 20 digits.

Or that the golden ratio, ?
, doesn't have a 5

in its first 20 digits.

Or that e
repeats the same four digits (1828) in its first ten digits (something that, in some sense, is far more unlikely than no zero in the first thirty digits of p ).

There is nothing particularly interesting in the digits of the decimal representation of irrational numbers. Or in the digits to any whole number base.

There is even less of interest in the decimal digits of p

as a particular transcendental number, except that so many people think there is something special about it.

Brought to you by the Campaign to Demystify p
: there is nothing mystical about p. 

There is nothing particularly interesting in the digits of the decimal representation of irrational numbers. Or in the digits to any whole number base.

especially


Let’s assume (as seems likely but is not proven at present) that p is a Normal Number[1] . Amongst other things, this means that the frequency of occurrence of any digit in its decimal expansion is precisely 1/10. This assumption is in accord with statistical analysis of many trillions of decimal places of p

and so is not an unreasonable one to take from a practical point of view.

We can use this to calculate the probability that there are no zeros in the first thirty digits of p
. In order for this to happen, zero cannot appear in the first place, a probability of 9/10 and also not in the second place, also a probability of 9/10

and so on. We get the overall probability to be:

(9/10)^30=9301030˜4.24%

So it is unlikely that no zero appears in the first thirty digits, but not exactly astronomically unlikely. It is only slightly less likely than a human picked at random being a left handed man.


    def is_prime(n): 
    	if n>1: 
    		divs=[k for k in range(2,n) if n%k==0] 
    		return len(divs)==0  
    	else: 
    		return False 
    		 
    def nth_prime(n): 
    	primes=[p for p in range(n*n+2) if is_prime(p)] 
    	return primes[n-1]