Example to Evaluate Basic Numeric Expressions (86688)

MORE INFORMATION

The example program listed below recognizes the following operators and subexpressions, listed by precedence from highest to lowest:

• Constants, function calls, parentheses
• Exponentiation ^
• Unary minus -
• Multiplication and division *, /
• Integer division \
• Integer modulus MOD
• Addition and subtraction +, -
• Relational operators =, <>, <, >, <=, >=
• NOT
• AND
• OR
• XOR
• EQV
• IMP

The precedence of unary minus "-" and operator "NOT" indicate the highest possible precedence of their operand. Unary minus and "NOT" may occur in an expression of any precedence. The following expressions illustrate the precedence rules for unary minus and "NOT".

   Expression        Value
   ----------        -----
    -1  ^  2          -1
   -(1  ^  2)         -1
   (-1) ^  2           1
     2  ^ -2          .25
    NOT  0  = 1       -1
    NOT (0  = 1)      -1
   (NOT  0) = 1        0
    NOT  0  AND 1      1
   (NOT  0) AND 1      1
    NOT (0  AND 1)    -1
				

The example program listed below accepts number constants written as decimal numbers with an optional fraction. For example, it accepts "123" and "123.4". It is possible to modify the program to recognize hexadecimal, scientific notation, or other formats.

This example program also recognizes the following functions: ABS, ATN, COS, EXP, FIX, INT, LOG, RND, SNG, SIN, SQR, and TAN.

Steps to Create Example Program

1. Run Visual Basic, or from the File menu, choose New Project (press ALT, F, N) if Visual Basic is already running. Form1 will be created by default.
2. Add a text box (Text1) and a command button (Command1) to Form1.
3. Set the Text property for Text1 to the null string (empty).
4. Enter the following code in the Command1 Click event procedure:

      Sub Command1_Click ()
          Dim n As Double
   
          If e_eval(Text1.Text, n) Then
            MsgBox Format$(n)
          End If
      End Sub
   
   					

5. Add the following code in the general Declarations section of Form1:

   ' To run this program in Visual Basic for MS-DOS, change the
   ' following Dim statements to DIM SHARED.
   '
   Dim e_input As String     ' Expression input string.
   Dim e_tok As String       ' Current token kind.
   Dim e_spelling As String  ' Current token spelling.
   Dim e_error As Integer    ' Tells if syntax error occurred.
   
   ' e_eval
   '   Evaluate a string containing an infix numeric expression.
   '   If successful, return true and place result in <value>.
   '   This is the top-level function in the expression evaluator.
   Function e_eval (ByVal s As String, value As Double) As Integer
      ' Initialize.
      e_error = 0
      e_input = s
      Call e_nxt
   
      ' Evaluate.
      value = e_prs(1)
   
      ' Check for unrecognized input.
      If e_tok <> "" And Not e_error Then
         MsgBox "syntax error, token = '" + e_spelling + "'"
      e_error = -1
      End If
   
      e_eval = Not e_error
   End Function
   
   ' e_prs
   '   Parse an expression, allowing operators of a specified
   '   precedence or higher. The lowest precedence is 1.
   '   This function gets tokens with e_nxt and recursively
   '   applies operator precedence rules.
   Function e_prs (p As Integer) As Double
      Dim n As Double    ' Return value.
      Dim fun As String  ' Function name.
   
      ' Parse expression that begins with a token (precedence 12).
      If e_tok = "num" Then
         ' number.
         n = Val(e_spelling)
         Call e_nxt
      ElseIf e_tok = "-" Then
         ' unary minus.
         Call e_nxt
         n = -e_prs(11)    ' Operand precedence 11.
      ElseIf e_tok = "not" Then
         ' logical NOT.
         Call e_nxt
         n = Not e_prs(6)  ' Operand precedence 6.
      ElseIf e_tok = "(" Then
         ' parentheses.
         Call e_nxt
         n = e_prs(1)
         Call e_match(")")
      ElseIf e_tok = "id" Then
         ' Function call.
         fun = e_spelling
         Call e_nxt
         Call e_match("(")
         n = e_prs(1)
         Call e_match(")")
         n = e_function(fun, n)
      Else
         If Not e_error Then
            MsgBox "syntax error, token = '" + e_spelling + "'"
            e_error = -1
         End If
      End If
   
      ' Parse binary operators.
   Do While Not e_error
     If 0 Then  ' To allow ElseIf .
     ElseIf p <= 11 And e_tok  = "^"  Then Call e_nxt: n = n ^   e_prs(12)
     ElseIf p <= 10 And e_tok  = "*"  Then Call e_nxt: n = n *   e_prs(11)
     ElseIf p <= 10 And e_tok = "/"   Then Call e_nxt: n = n /   e_prs(11)
     ElseIf p <= 9  And e_tok = "\"   Then Call e_nxt: n = n \   e_prs(10)
     ElseIf p <= 8  And e_tok = "mod" Then Call e_nxt: n = n Mod e_prs(9)
     ElseIf p <= 7  And e_tok = "+"   Then Call e_nxt: n = n +    e_prs(8)
     ElseIf p <= 7  And e_tok = "-"   Then Call e_nxt: n = n -    e_prs(8)
     ElseIf p <= 6  And e_tok = "="   Then Call e_nxt: n = n =    e_prs(7)
     ElseIf p <= 6  And e_tok = "<"   Then Call e_nxt: n = n <    e_prs(7)
     ElseIf p <= 6  And e_tok = ">"   Then Call e_nxt: n = n >    e_prs(7)
     ElseIf p <= 6  And e_tok = "<>"  Then Call e_nxt: n = n <>   e_prs(7)
     ElseIf p <= 6  And e_tok = "<="  Then Call e_nxt: n = n <=   e_prs(7)
     ElseIf p <= 6  And e_tok = ">="  Then Call e_nxt: n = n >=   e_prs(7)
     ElseIf p <= 5  And e_tok = "and" Then Call e_nxt: n = n And  e_prs(6)
     ElseIf p <= 4  And e_tok = "or"  Then Call e_nxt: n = n Or   e_prs(5)
     ElseIf p <= 3  And e_tok = "xor" Then Call e_nxt: n = n Xor  e_prs(4)
     ElseIf p <= 2  And e_tok = "eqv" Then Call e_nxt: n = n Eqv  e_prs(3)
     ElseIf p <= 1  And e_tok = "imp" Then Call e_nxt: n = n Imp  e_prs(2)
     Else
          Exit Do
     End If
    Loop
   
      e_prs = n
   End Function
   
   ' e_function.
   '   Evaluate a function. This is a helper function to simplify
   '   e_prs.
   Function e_function (fun As String, arg As Double) As Double
      Dim n As Double
   
      Select Case LCase$(fun)
      Case "abs": n = Abs(arg)
      Case "atn": n = Atn(arg)
      Case "cos": n = Cos(arg)
      Case "exp": n = Exp(arg)
      Case "fix": n = Fix(arg)
      Case "int": n = Int(arg)
      Case "log": n = Log(arg)
      Case "rnd": n = Rnd(arg)
      Case "sgn": n = Sgn(arg)
      Case "sin": n = Sin(arg)
      Case "sqr": n = Sqr(arg)
      Case "tan": n = Tan(arg)
      Case Else
         If Not e_error Then
            MsgBox "undefined function '" + fun + "'"
            e_error = -1
         End If
      End Select
   
      e_function = n
   End Function
   
   ' e_nxt
   '   Get the next token into e_tok and e_spelling and remove the
   '   token from e_input.
   '   This function groups the input into "words" like numbers,
   '   operators and function names.
   Sub e_nxt ()
      Dim is_keyword As Integer
      Dim c As String  ' Current input character.
   
      e_tok = ""
      e_spelling = ""
   
      ' Skip whitespace.
      Do
         c = Left$(e_input, 1)
         e_input = Mid$(e_input, 2)
      Loop While c = " " Or c = Chr$(9) Or c = Chr$(13) Or c = Chr$(10)
   
      Select Case LCase$(c)
   
      ' Number constant. Modify this to support hexadecimal, etc.
      Case "0" To "9", "."
         e_tok = "num"
         Do
            e_spelling = e_spelling + c
            c = Left$(e_input, 1)
            e_input = Mid$(e_input, 2)
         Loop While (c >= "0" And c <= "9") Or c = "."
         e_input = c + e_input
   
      ' Identifier or keyword.
      Case "a" To "z", "_"
         e_tok = "id"
         Do
            e_spelling = e_spelling + c
            c = LCase$(Left$(e_input, 1))
            e_input = Mid$(e_input, 2)
            is_id% = (c >= "a" And c <= "z")
            is_id% = is_id% Or c = "_" Or (c >= "0" And c <= "9")
         Loop While is_id%
         e_input = c + e_input
   
         ' Check for keyword.
         is_keyword = -1
         Select Case LCase$(e_spelling)
            Case "and"
            Case "eqv"
            Case "imp"
            Case "mod"
            Case "not"
            Case "or"
            Case "xor"
            Case Else: is_keyword = 0
         End Select
         If is_keyword Then
            e_tok = LCase$(e_spelling)
         End If
   
      ' Check for <=, >=, <>.
      Case "<", ">"
         e_tok = c
         c = Left$(e_input, 1)
         If c = "=" Or c = ">" Then
            e_tok = e_tok + c
            e_input = Mid$(e_input, 2)
         End If
   
      ' Single character token.
      Case Else
         e_tok = c
      End Select
   
       If e_spelling = "" Then
          e_spelling = e_tok
      End If
   End Sub
   
   ' e_match
   '   Check the current token and skip past it.
   '   This function helps with syntax checking.
   Sub e_match (token As String)
      If Not e_error And e_tok <> token Then
         MsgBox "expected " + token + ", got '" + e_spelling + "'"
         e_error = -1
      End If
      Call e_nxt
   End Sub
   					

6. Press F5 to run the program. Type an expression into Text1 such as "1+2*3^4". Click Command1.

The program displays the result, 163 in this case.