How To Use TFPExpressionParser
│ English (en) │ suomi (fi) │
TFPExpressionParser allows to analyze and calculate expressions such as
sin(x)*cos(2*x) for any value of the variable
x. Besides mathematical expressions it can also handle boolean, string formulas, date/time values etc. Even user-provided functions can be linked in.
It belongs to FPC Free Component Library (FCL) and is implemented in the unit
(fpc_source_dir)/packages/fcl-base/src. Just add
fpexprpars to the uses clauses to get access to its functionality. See the file "fpexprpars.txt" (in
(fpc_source_dir)/packages/fcl-base/examples) for a short documenation.
- 1 Creating the parser
- 2 Built-in categories
- 3 Expressions
- 4 Adding user-defined functions
Creating the parser
You apply the parser by creating an instance like this:
uses fpexprpars; var FParser: TFPExpressionParser; begin FParser := TFpExpressionParser.Create(self); // ... do something (see below)
If this is called from a method of a form, "self" points to the form. Since the parser inherits from
TComponent, there is no need to destroy it explicitly since its owner, the form, will do it. On the other hand, it is also possible to create the parser from anywhere in a program without a form or even class being involved; in this case use
nil as the owner of the parser, but don't forget to
.Free the parser after its usage:
uses fpexprpars; var FParser: TFPExpressionParser; begin FParser := TFPExpressionParser.Create(nil); try // ... do something (see below) finally FParser.Free; end; end;
The parser is designed in a very flexible way, but the default parser is quite dumb. You have to specify which kind of expressions it will accept. This is done by adding the corresponding identifier to the set of built-in categories. They are accessible by the parser's property
type TBuiltInCategory = (bcStrings, bcDateTime, bcMath, bcBoolean, bcConversion, bcData, bcVaria, bcUser, bcAggregate); TBuiltInCategories = set of TBuiltInCategory;
Here is a collection of the built-in symbols which can be used by adding categories to the parser's
BuiltIns - it should be clear to anybody who "speaks" Pascal what these symbols mean...
IFxxxsymbols have the same effect as fpc's
IfThenfor string (
IFS), floating point (
IFF), date/time (
IFD), or integer (
bcUser are not used anywhere within fpexprpars. The last section gives instructions how to extend the parser with more functions.
In order to use a mathematical expression the option
bcMath has to be added to the parser's
FParser.Builtins := [bcMath]; // or FParser.Builtins := FParser.Builtins + [bcMath];
An expression with constants
As a first example we have the parser calculate a very simple expression
The first step is to tell the parser which expression is to be calculated. There is a property
Expression for this purpose:
FParser.Expression := '1+1';
var parserResult: TFPExpressionResult; begin .... parserResult := FParser.Evaluate; // or: FParser.EvaluateExpression(parserResult);
What is that mysterious
TFPExpressionResult? Since the parser is very flexible and can deal with numbers, strings, date/times or booleans there must be a more complex data type which returns a calculation result:
type TResultType = (rtBoolean, rtInteger, rtFloat, tDateTime, rtString); TFPExpressionResult = record ResString : String; Case ResultType : TResultType of rtBoolean : (ResBoolean : Boolean); rtInteger : (ResInteger : Int64); rtFloat : (ResFloat : TExprFloat); rtDateTime : (ResDateTime : TDatetime); rtString : (); end;
ResultType signals which one of the data fields is valid. It is important to understand this since the expression parser is very strict on data types.
In our example, we are adding two integers, therefore the result is an integer as well. If, on the other had, we had used the expression
"1.0 + 1", the first number would have been a floating point value, and the result would have been a float! Therefore, always have a look at the member
ResultType of the
TFPExpressionResult before picking the result. To simplify the usage of the expression result data type,
fpexprpars exposes a function
ArgToFloat which gets the entire expression result record as a parameter and selects the right component if a floating point result is expected:
var parserResult: TFPExpressionResult; resultValue: Double; ... parserResult := FParser.Evaluate; // or: FParser.EvaluateExpression(parserResult); resultValue := ArgToFloat(parserResult);
An expression with a variable
In this example, we calculate the value of
x = 0.5.
At first we have to define the variables. We have only one,
x. The parser has a method
AddFloatVariable to declare a floating point variable; there are also methods
for boolean, string and date/time variables, respectively.
Each one of these methods expects the name of the variable along with its default value. For the sample function
sin(x)*cos(2*x) we just call:
0.5 is entered here as a default value because that is the argument at which we want to calculate the expression (it will be shown below how to modify a variable). From now on, the parser will use this number whenever it finds the variable
x in the expression.
Defining the expression
In the next step, the expression string has to be passed to the parser:
FParser.Expression := 'sin(x)*cos(2*x)';
It is essential to call this after setting up of the variables because the parser needs to know the variables for analyzing the expression.
Calculating the expression
This is done as before with the constant expression - here is a complete procedure which shows the equation and its result in a message box:
var FParser: TFPExpressionParser; resultValue: Double; begin FParser := TFPExpressionParser.Create(nil); try FParser.BuiltIns := [bcMath]; FParser.Identifiers.AddFloatVariable('x', 0.5); FParser.Expression := 'sin(x)*cos(2*x)'; resultValue := FParser.Evaluate.ResFloat; // or: resultValue := ArgToFloat(FParser.Evaluate); ShowMessage(FParser.Expression + ' = ' + FloatToStr(resultValue)); finally FParser.Free; end; end;
x always has the value 0.5 - it behaves like a constant, we could have used the expression
"sin(0.5)*cos(2*0.5)" as well.
To make it behave more like a "variable", we now calculate the test function for the
x values between -10 and 10 at integer steps.
The main question is: How to replace the value assigned to a variable? There are several possibilities - all of them require the internal variable
TFPExprIdentifierDef) which exposes various ways to access variables and their properties:
- Use the return value of the
- Seek an identifier by calling
FindIdentifierByNamewith the variable name as a parameter.
- Access the identifier from the
Identifierscollection of the parser by using the known index of the variable: We had added
xas the only variable, therefore, it must be at index 0.
Identifier is known, the value of the variable can be changed by accessing the property
AsDateTime etc. accordingly):
var FParser: TFPExpressionParser; argument: TFPExprIdentifierDef; s: string; x: integer; f: double; begin s:=''; FParser := TFPExpressionParser.Create(nil); try // Enable the use of mathematical expressions FParser.BuiltIns := [bcMath]; // Add the function argument argument := FParser.Identifiers.AddFloatVariable('x', 0.0); // Define the function, using the argument name x as defined above FParser.Expression := 'sin(x)*cos(2*x)'; // Calculate some function values for x := -10 to 10 do begin argument.AsFloat := x; // Set the function argument value f := FParser.Evaluate.ResFloat; // Calculate the function value s := s + format('x[%d]:[%g]' + LineEnding, [x,f]); // Demo output to display the result end; // Show the result ShowMessage(s); finally FParser.Free; end; end;
The expressions discussed above show that standard operators
<=, etc., can be used to setup an expression. Additionally, in recent FPC versions, the operator
^ is available for calculating the power, and
mod for the remainder of integer divisions (modulo).
In addition to "normal" function the parser supports also "aggregate" functions which are repeatedly applied to a variable, e.g. sum(x) which adds up all the values assigned to the variable x. These functions are available:
- min(x) - Calculate the minimum of all values assigned to x
- max(x) - Calculate the maximum of all values assigned to x
- sum(x) - Calculate the sum of all values assigned to x
- avg(x) - Calculate the average of the values assigned to x
- count(x) - Count the numbers assigned to x
In order to have aggregate functions available the category
bcAggregate must be added to the
BuiltIns of the parser. Next step is to define a variable to which the aggregate function will be applied. The aggregation process must be initialized by calling the parser method
InitAggregate; and whenever the variable value is changed the method
UpdateAggregate must be alled.
Here is an example which calculates the sum of the elements of an array:
uses fpexprpars; const Data: array[0..5] of Double = (1.221, 3.4, -1.0, -0.221, -3.0, -0.4); var FParser: TFPExpressionParser; xVar: TFPExprIdentifierDef; x: Double; begin FParser := TFPExpressionParser.Create(nil); try FParser.BuiltIns := [bcAggregate]; xVar := FParser.Identifiers.AddFloatVariable('x', 0); FParser.Expression := 'sum(x)'; FParser.InitAggregate; WriteLn('Sum of'); for x in Data do begin xVar.AsFloat := x; WriteLn(xVar.AsFloat:10:3); FParser.UpdateAggregate; end; WriteLn('----------'); WriteLn(FParser.Evaluate.ResFloat:10:3); finally FParser.Free; end; ReadLn; end.
Adding user-defined functions
The default parser only knows the built-in functions mentioned above. One of the strengths of of the expression parser is that it is very easy to extend to include other functions. This can be done by calling the method
FParser.Identifiers.AddFunction('tan', 'F', 'F', @ExprTan);
In this example, we add the function tan(x) by specifying its name as it will be called in the function expressions (first parameter), the type of the result values (second parameter, "F" = float, "I" = integer, "D" = date/time, "S" = string, or "B" = boolean) and the type of the input values (third parameter, same logic). If a function accepts several input parameters the type of each one must be specified, e.g. by 'FF' for two floating point values, or 'FI' for a first float and a second integer parameter. The last parameter points to the function which is called whenever "tan" is found in the expression string. Since this function has a particular syntax we have to implement it in our own source code:
procedure ExprTan(var Result: TFPExpressionResult; Const Args: TExprParameterArray); var x: Double; begin x := ArgToFloat(Args); Result.resFloat := tan(x); end;
The result of the calculation is returned as parameter "Result" which is a TFPExpressionResult that we met above. The arguments for the calculation are passed by Args which is just an array of TFPExpressionResult values - again because parameters can have several data types. The term TFPExpressionResults is maybe a bit misleading here, because this array holds all the *input* parameters as specified by the input types of the AddFunction method.
When, in fpc 3.3.1 or later, the input parameter symbol string of the AddFunction method ends with a '+' then parameters with the previous type can be repeated as often as needed; this way a function with a variable parameter count can be implemented. In the following example, we add the function SumOf which adds up as many values as provided:
procedure ExprSumOf(var Result: TFPExpressionResult; Const Args: TExprParameterArray); var sum: Double; arg: TFPExpressionResult; begin sum := 0; for arg in Args do sum := sum + ArgToFloat(arg); Result.ResFloat := sum; end; begin ... FParser.Identifiers.AddFunction('SumOf', 'F', 'F+', @ExprSumOf); FParser.Expression := 'SumOf(-1,2,3,4.1)'; // arbitrary number of arguments! WriteLn(FParser.Evaluate.ResFloat:0:3); ...