TMathParser
Contents
Review
There is a newversion of parser available (download).
The component isintended for mathematics calculations. It contains standard set of mathematicsfunctions, such as sin or sqrt. It also contains standard set of types, such asbyte or word which are used for specifying the functions. It is possible tocreate your own functions and types. The parser works with the high speed -about ten million operations per second for simple mathematics formulas. Itcreates binary representation of formula (script) and makes all the followingcalculations by the script. There are no limitations for the formula; it couldhave any length and any amount of embedded formulas. Embedded formula isexpression that is located between brackets and has increased calculationpriority. The parser implements many features, including methods forsimplifying the formula and support of function with unlimited parameters.
It implementsadditional features, including support of function with unlimited parameters.
As usual it iseasy to use –
1) Place TMathParsercomponent and some interface controls on the form:
2) Use it:
3) Expression ismathematics formula which can be constructed using the elements:
- +: operand, executes adding operation
- -: operand, executes subtraction operation
- *: function, executes multiplying operation
- /: function, executes division operation
- Sqrt: functions, root of a number. Root can have any degree
- Div: functions, executes integer division operation
- Mod: functions, executes remainder operation
- Int: function, returns the integer part of a number
- Frac: function, returns the fractional part of a number
- Random: function, returns random number within the range 0 <= value < 1
- Trunc: function, truncates a number to an integer
- Round: function, returns the value rounded to the nearest whole number
- Sin: function, returns the sine of the angle in radians
- ArcSin: function, returns the inverse sine of a number
- Sinh: function, returns the hyperbolic sine of an angle
- ArcSinh: function, returns the inverse hyperbolic sine of a number
- Cos: function, returns the cosine of the angle in radians
- ArcCos: function, returns the inverse cosine of a number
- Cosh: function, returns the hyperbolic cosine of an angle
- ArcCosh: function, returns the inverse hyperbolic cosine of a number
- Tan: function, returns the tangent of the angle
- ArcTan: function, returns the arctangent of a number
- Tanh: function, returns the hyperbolic tangent of an angle
- ArcTanh: function, the inverse hyperbolic tangent of a number
- CoTan: function, returns the cotangent of the angle
- ArcCoTan: function, returns the inverse cotangent of a number
- CoTanh: function, returns the hyperbolic cotangent of an angle
- ArcCoTanh: function, the inverse hyperbolic cotangent of a number
- Sec: function, returns the secant of an angle
- ArcSec: function, returns the inverse secant of a number
- Sech: function, returns the hyperbolic secant of an angle
- ArcSech: function, returns the inverse hyperbolic secant of a number
- Csc: function, returns the cosecant of an angle
- ArcCsc: function, returns the inverse cosecant of a number
- Csch: function, returns the hyperbolic cosecant of an angle
- ArcCsch: function, returns the inverse hyperbolic secant of a number
- Abs: function, returns an absolute value
- Ln: function, returns the natural log of an expression
- Lg: function, returns log base 10
- Log: function, returns the log of expression for a specified base
- Pi: function, returns 3.1415926535897932385
- Exp: function, returns the exponential of an expression
- !: function, returns factorial of an expression
- ^: function, raises expression to any power
- ArcTan2 [Y, X: Double] function, calculates ArcTan(Y/X), and returns an angle in the correct quadrant. The values of X and Y must be between –2^64 and 2^64. Inaddition, the value of X can’t be 0. The return value will fall in the range from -Pi to Pi radians.
- Hypot [X, Y: Double] function, returns the length of the hypotenuse of a right triangle. Specify the lengths of the sides adjacent to the right angle in X and Y. Hypot usesthe formula Sqrt(X**2 + Y**2)
- RadToDeg function, converts radians to degrees
- RadToGrad function, converts radians to grads
- RadToCycle function, converts radians to cycles
- DegToRad function, returns the value of a degree measurement expressed in radians
- DegToGrad function, returns the value of a degree measurement expressed in grads
- DegToCycle function, returns the value of a degree measurement expressed in cycles
- GradToRad function, converts grad measurements to radians
- GradToDeg function, converts grad measurements to degrees
- GradToCycle function, converts grad measurements to cycles
- CycleToRad function, converts an angle measurement from cycles to radians
- CycleToDeg function, converts an angle measurement from cycles to degrees
- CycleToGrad function, converts an angle measurement from cycles to grads.
- LnXP1 function, returns the natural log of (X+1)
- Log10 function, calculates log base 10
- Log2 function, calculates log base 2
- IntPower [Base: Double; Exponent: Integer] function, calculates the integral power of a base value
- Power [Base: Double; Exponent: Double] function, Raises Base to any power
- Ldexp [X: Double; P: Double] function, calculates X times (2 to the power of P)
- Ceil function, rounds variables up toward positive infinity
- Floor function, rounds variables toward negative infinity
- Poly [X: Double; Coefficients(1)..Coefficients(N): Double] function, evaluates a uniform polynomial of one variable at the value X
- Mean [Data(1)..Data(N): Double] function, returns the average of all values in an array
- Sum [Data(1)..Data(N): Double] function, returns the sum of the elements in an array
- SumInt [Data(1)..Data(N): Integer] function, returns the sum of the elements in an integer array
- SumOfSquares [Data(1)..Data(N): Double] function, returns the sum of the squared values from a data array
- MinValue [Data(1)..Data(N): Double] function, returns smallest signed value in an array
- MinIntValue [Data(1)..Data(N): Integer] function, returns the smallest signed value in an integer array
- Min [A,B: Double] function, returns the lesser of two numeric values
- MaxValue [Data(1)..Data(N): Double] function, returns the largest signed value in an array
- MaxIntValue [Data(1)..Data(N): Integer] function, returns the largest signed value in an integer array
- Max [A,B: Double] function, returns the greater of two numeric values
- StdDev [Data(1)..Data(N): Double] function, returns the sample standard deviation for elements in an array
- PopnStdDev [Data(1)..Data(N): Double] function, calculates the population standard deviation
- Variance [Data(1)..Data(N): Double] function, calculates statistical sample variance from an array of data
- PopnVariance [Data(1)..Data(N): Double] function, calculates the population variance
- TotalVariance [Data(1)..Data(N): Double] function, returns the statistical variance from an array of values
- Norm [Data(1)..Data(N): Double] function, returns the Euclidean 'L-2' norm
- RandG [Mean, StdDev: Double] function, generates random numbers with Gaussian distribution
- RandomRange [AFrom, ATo: Integer] function, returns a random integer from a specified range
- RandomFrom [Value(1)..Value(N): Double] function, returns a randomly selected element from an array
- EnsureRange [AValue, AMin, AMax: Double] function, returns the closest value to a specified value within a specified range
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Optimization
Some mathematicexpressions can be optimized. Optimization is simplifying of mathematicexpression (if possible) at binary level; the result is an increase inevaluation speed. You need to call just one function to optimize theexpression:
The optimal scriptrepresents a simple number. If OptimizeScript function called and OptimalScriptfunction returns false, this does not mean the script is not changed. Probablymany parts of the script become optimal in contrast to the whole script. As itis shown above, function random makes full optimization impossible.
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Creating the function
It is easy tocreate your own function. To do this you need first to declare procedure ofTFunctionEvent type in your application.
TFunctionEvent = procedure(FunctionIndex:Integer; TypeIndex: Integer;
out Value:Double; LValue, RValue: Double; Parameters: TParameters;
varDone: Boolean) of object;
Procedure of thistype calls each time it is necessary to execute any function.
Then you registeryour function by method:
procedure RegisterFunction(var Index:Integer; const AName: string;
ARequireValue1, ARequireValue2, AOptimizable: Boolean;
AParameterCount: Integer); virtual;
procedure RegisterFunction(var Index:Integer; const AName: string;
ARequireValue1, ARequireValue2, AOptimizable: Boolean;
AParameterCount: Integer); virtual;
IfRegisterFunction succeeded then FunctionIndex is the index of the function;otherwise FunctionIndex is set to -1. AName is a new function name.ARequireValue1, ARequireValue2 parameters specify whether or not the newfunction needs expressions before or after itself. For example, the standardfunction * (multiplying) needs both parameters (2 * 3, where 2 and 3 are in arole of expression); and function Sqrt needs the parameter only after itself.Function Pi does not need any parameters, it returns 3.1415926535897932385.AOptimizable parameter specifies whether it is possible to optimize thefunction. For example, it is possible to optimize standard function Cos; butyou cannot optimize function Random because it returns different values eachtime it is called.
If AParameterCountparameter is more than zero, then the function needs AParameterCount parametersafter itself, which are enclosed in square braces. This also means that thefunction is of new type and cannot require parameters before or after itself,unlike standard function does. Any of the parameters in square braces can be eithera string variable or mathematic expression; in case if it is a mathematicexpression, it participates in optimization process too.
procedure CustomFunction(FunctionIndex: Integer;TypeIndex: Integer;
out Value:Double; LValue, RValue: Double; Parameters: TParameters;
varDone: Boolean);
This procedure iscalled each time it is necessary to execute any function. Using it allows you tooverwrite the standard functions behavior as well. FunctionIndex is the indexof the function, TypeIndex is the index of the type (we will see later how touse types). The result of execution must be placed in Value parameter. As itwas mentioned before, the function may require the expression either after orbefore itself. Results of these expressions are stored in LValue (expressionbefore current function) and RValue (expression after current function)parameters. Parameters are an array of TParameter values:
TParameter = record
TypeIndex:Integer;
caseByte of
0: (Value: Double);
1: (S: ShortString);
end;
TParameters = arrayof TParameter;
This recordcontains the value of the parameter and its type.
As a default Doneparameter is False. If procedure handles the current function, it must set Doneparameter to true.
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Non-standard function withparameters
The next exampleshows how to use non-standard function with parameters:
This sampleimplements two Delphi functions: StrToInt whichconverts a string that represents an integer and Power(please note that Power function is alreadyincluded in standard functions set and its behavior is changed in the sample;in such a manner it is possible to overwrite the behavior of any function)which raises a number to any power. You can see their description in Delphi help. Both functions need parameters. First function needs one string parameter andthe second one needs two numeric parameters.
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Types
Parser lets youuse types. The sample below shows how to work with them:
As it is shownabove you can specify a type within a number of parameters of non-standardfunction. You can also specify type for every standard function.
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Building the graphs
And finally theold colorful sample which allows building the graphs:
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Downloads
These downloads below are for Delphi 7. There is apackage with components and samples for Delphi 5 here; the same package for Delphi 6 is here.
