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math formula parsers

Posted on 2002-04-29
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hi does anyonw know a free math formula parser component? help! thanks! :)
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by:AvonWyss
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You can find a bunch here:
http://www.torry.net/expressions.htm

For free ones, look at the entries markes with FW (Freeware) or FWS (Freeware with source).
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by:zebada
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There's one here http://www.blacky.co.nz/free/index.htm
called Expr - about halfway down.

If that link is broken (it often is) then go to this link: http://www.geocities.com/freeblacky
Download the expr.zip file which is written in Delphi.
Note: the expression.zip is written in java not Delphi.

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by:dabestprogrammerindauniverse
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thanks! but actually, what i need is also a math formula evaluator that can also do summations :(
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Accepted Solution

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Hamatoma earned 100 total points
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Hi,

I have written this class, modify and/or use it!

unit HmLbCalc;

interface

uses
      Math, HmLbType;

type
      T_Operator = (opUndef,
            opPlus, opMinus,
            opTimes, opDiv, opModulo,
            opPower
            );

const
C_MaxFloatStack = 64;

type
T_FloatStack = class
      FStack: array [0..C_MaxFloatStack] of extended;
      FTop: integer;
      constructor Create;
      procedure Push (Val: extended);
      function Pop: extended;
      function Top: extended;
      function IsEmpty: boolean;
      end;

const
C_MaxOperatorStack = 64;

C_StdPrecision = -2;

type
T_OperatorStack = class
      FStack: array [0..C_MaxOperatorStack] of T_Operator;
      FTop: integer;
      constructor Create;
      procedure Push (Val: T_Operator);
      function Pop: T_Operator;
      function Top: T_Operator;
      function IsEmpty: boolean;
      function GetLevel: integer;
      end;

T_Calculator = class
      private
      FMemory: array [0..9] of extended;
      FResult: extended;
      FPrecision: integer;
      FExponentNotation: boolean;
      FOperandStack: T_FloatStack;
      FOperatorStack: T_OperatorStack;
      public
      constructor Create;
      function Expr (ExspectedEnd: char; const Line: string;
            var nPos: integer): T_ResultString;
      function FullExpr (const Line: string; var Val: extended): T_ResultString;
      function GetResult: extended; overload;
      function GetResult (Precision: integer): string; overload;
      function StrToOperator (const OpStr: string): T_Operator;
      function IsOperand (const Op: string; var Val: extended): boolean;
      function GetMemory (Ix: integer): extended;
      procedure PutMemory (Ix: integer; Val: extended);
      function Priority (Op: T_Operator): integer;
      function Reduce: T_ResultString;
      procedure SetPrecision (Digits: integer);
      procedure SetExponentNotation (Exponent: boolean);
      end; // T_Calculator
implementation

uses
      SysUtils,
      HmLbStr;

function NextExprToken (
      const Str: string;
      var StartIx: integer;
      var Token: string
      ): integer;
var
      Len, StrLen: integer;
      Dummy: extended;
begin
      StrLen := Length (Str);
      while (StartIx <= StrLen) and (Str [StartIx] <= ' ') do
            Inc (StartIx);

      Len := 0;
      if StartIx <= StrLen
      then case Str [StartIx] of
            '0'..'9':
                  Len := AToFloat (Str, StartIx, Dummy);
            'a'..'z', 'A'..'Z', '_':
                  begin
                  while (StartIx + Len <= StrLen)
                              and (Str [StartIx + Len] in ['0'..'9', 'a'..'z', 'A'..'Z', '_']) do
                        Inc (Len);
                  end;
            else
                  Len := 1;
            end; // case
      Token := copy (Str, StartIx, Len);
      Inc (StartIx, Len);
      Result := Len;
      while (StartIx <= StrLen) and (Str [StartIx] <= ' ') do
            Inc (StartIx);
end;

constructor T_FloatStack.Create;
begin
      FTop := -1;
end; // Create

procedure T_FloatStack.Push (Val: extended);
begin
      if FTop >= C_MaxFloatStack
      then raise Exception.Create ('T_FloatStack.Push: \berlauf bei '
            + IntToStr (C_MaxFloatStack));
      Inc (FTop);
      FStack [FTop] := Val;
end; // Push

function T_FloatStack.Pop: extended;
begin
      if FTop < 0
      then raise Exception.Create ('T_FloatStack.Pop: Unterlauf');
      Result := FStack [FTop];
      Dec (FTop);
end; // Push

function T_FloatStack.Top: extended;
begin
      if FTop < 0
      then raise Exception.Create ('T_FloatStack.Top: Unterlauf');
      Result := FStack [FTop];
end; // Top

function T_FloatStack.IsEmpty: boolean;
begin
      Result := FTop < 0;
end; // IsEmpty



//-------------------------------------------------------------------
constructor T_OperatorStack.Create;
begin
      FTop := -1;
end; // Create

procedure T_OperatorStack.Push (Val: T_Operator);
begin
      if FTop >= C_MaxOperatorStack
      then raise Exception.Create ('T_OperatorStack.Push: \berlauf bei '
            + IntToStr (C_MaxOperatorStack));
      Inc (FTop);
      FStack [FTop] := Val;
end; // Push

function T_OperatorStack.Pop: T_Operator;
begin
      if FTop < 0
      then raise Exception.Create ('T_OperatorStack.Pop: Unterlauf');
      Result := FStack [FTop];
      Dec (FTop);
end; // Push

function T_OperatorStack.Top: T_Operator;
begin
      if FTop < 0
      then raise Exception.Create ('T_OperatorStack.Top: Unterlauf');
      Result := FStack [FTop];
end; // Top

function T_OperatorStack.IsEmpty: boolean;
begin
      Result := FTop < 0;
end; // IsEmpty

function T_OperatorStack.GetLevel: integer;
begin
      Result := FTop;
end; // GetLevel


// --------------------------------------------------------------------
constructor T_Calculator.Create;
begin
      FResult := 0;
      FPrecision := -1;
      FOperandStack := T_FloatStack.Create;
      FOperatorStack := T_OperatorStack.Create;
end; // Create

function T_Calculator.StrToOperator (
      const OpStr: string
      ): T_Operator;
begin
      if OpStr = '+'
      then Result := opPlus
      else if OpStr = '-'
      then Result := opMinus
      else if OpStr = '*'
      then Result := opTimes
      else if OpStr = '/'
      then Result := opDiv
      else if OpStr = '%'
      then Result := opModulo
      else if OpStr = '^'
      then Result := opPower
      else Result := opUndef;
end; // StrToOp

function T_Calculator.IsOperand (
      const Op: string;
      var Val: extended
      ): boolean;
var
      Len: integer;
begin
      Result := true;
      if (Length (Op) = 2) and (Op [1] = 'M') and (Op [2] in ['0' .. '9'])
      then Val := GetMemory (ord (Op [2]) - ord ('0'))
      else begin
            Len := AToFloat (Op, 1, Val);
            Result := Len = Length (Op);
            end;
end; // IsOperand


function T_Calculator.Expr (
      ExspectedEnd: char;
      const Line: string;
      var nPos: integer
      ): T_ResultString;
var
      Token: string;
      Op1: extended;
      Op: T_Operator;
      Minus: boolean;
      LineLen: integer;
      Level: integer;
begin
      Level := FOperatorStack.GetLevel;
      Result := '';
      LineLen := Length (Line);

      repeat // until (Result <> '') or (nPos > LineLength);
            Minus := false;
            repeat
                  if NextExprToken (Line, nPos, Token) = 0
                  then break;
                  Op := StrToOperator (Token);
                  if Op = opMinus
                  then Minus := not Minus;
            until not (Op in [opMinus, opPlus]);

            if Token = ''
            then begin
                  Result := 'Operand erwartet';
                  break;
                  end;

            if Token = '('
            then begin
                  Result := Expr (')', Line, nPos);
                  Op1 := FOperandStack.Pop;
                  end // Token = Klammer
            else if not IsOperand (Token, Op1)
            then Result := 'Operand erwartet: ' + Token;

            if (Result <> '') or (Token = '')
            then break;

            if Minus
            then Op1 := - Op1;
            FOperandStack.Push (Op1);

            if (NextExprToken (Line, nPos, Token) = 0)
                  or (Token [1] in [')', ','])
            then break;

            Op := StrToOperator (Token);
            if Op = OpUndef
            then begin
                  Result := 'unbekanntes Rechenzeichen: ' + Token;
                  break;
                  end;
            while (Result = '') and not FOperatorStack.IsEmpty
                        and (Priority (FOperatorStack.Top) >= Priority (Op)) do
                  Result := Reduce;

            if (Result = '') and (nPos > LineLen) or (Line [nPos] = ')')
            then begin
                  Inc (nPos);
                  break;
                  end;
            FOperatorStack.Push (Op);
      until (Result <> '') or (nPos > LineLen);
      if (ExspectedEnd = #0) and (Token = '') or (Token = ExspectedEnd)
      then begin
            while FOperatorStack.GetLevel > Level do
                  Reduce;
            end
      else if ExspectedEnd = #0
            then Result := '<Eingabeende> erwartet statt: ' + Token
            else Result := ExspectedEnd + ' erwartet statt: ' + Token;
end; // Expr

function T_Calculator.FullExpr (
      const Line: string;
      var Val: extended
      ): T_ResultString;
var
      nPos: integer;
begin
      nPos := 1;
      Result := Expr (#0, Line, nPos);
      if (Result = '') and (nPos < Length (Line))
      then Result := 'Elemente nach Ausdrucksende: ' + copy (Line, nPos, 255)
      else begin
            FResult :=FOperandStack.Pop;
            Val := FResult;
            end;
end; // FullExpr

function T_Calculator.GetResult: extended;
begin
      Result := FResult;
end; // GetResult

function T_Calculator.GetResult (
      Precision: integer
      ): string;
var
      FormatStr: string;
begin
      if Precision = C_StdPrecision
      then Precision := FPrecision;

      if Precision < 0
      then FormatStr := '%g'
      else if FExponentNotation or (FResult > 1E16) or (FResult < -1E16)
            then FormatStr := '%.' + IntToStr (Precision + 1) + 'e'
            else FormatStr := '%.' + IntToStr (Precision) + 'f';
      Result := Format (Formatstr, [FResult])
end; // GetResult

function T_Calculator.GetMemory (Ix: integer): extended;
begin
      Result := FMemory [Ix];
end; // GetMemory

procedure T_Calculator.PutMemory (Ix: integer; Val: extended);
begin
      FMemory [Ix] := Val;
end; // PutMemory

function T_Calculator.Priority (
      Op: T_Operator
      ): integer;
begin
      case Op of
      opPlus, opMinus:
            Result := 1;
      opTimes, opDiv, opModulo:
            Result := 2;
      opProcent, opProcentPlus, opProcentMinus, opProcentFrom,
      opProcentPlusFrom, opProcentMinusFrom, opProcentBase:
            Result := 3;
      opPower:
            Result := 4;
      else
            Result := -1;
      end;
end; // Priority

function T_Calculator.Reduce: T_ResultString;
var
      Op1, Op2: extended;
      Op: T_Operator;
begin
      Result := '';
      Op2 := FOperandStack.Pop;
      Op1 := FOperandStack.Pop;
      Op := FOperatorStack.Pop;
      case Op of
      opPlus:      
            Op1 := Op1 + Op2;
      opMinus:      
            Op1 := Op1 - Op2;
      opTimes:      
            Op1 := Op1 * Op2;
      opDiv:      
            if Op2 = 0.0
            then Result := 'Division durch 0'
            else Op1 := Op1 / Op2;
      opModulo:
            if trunc (Op2) <= 0
            then Result := 'Modulus <= 0: ' + Format ('%f', [Op2])
            else Op1 := trunc (Op1) mod trunc (Op2);
      opPower:
            if Op1 < 0
            then Result := 'Basis < 0: ' + Format ('%f', [Op1])
            else Op1 := power (Op1, Op2);
      else
            Result := 'Unbekannter Operator: ' + IntToStr (ord (Op));
      end;
      if Result = ''
      then FOperandStack.Push (Op1);
end; // Reduce


                         
end.
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