Friday, April 13, 2012

Math parsing function/component anyone?

I'm looking for a reasonably light-weight, simple and fast math function parser. It should not be a DLL. I need it to work on Windows, MacOSX and iOS. I would use it in a demo I want to build.

It must be able to parse and evaluate functions of (at least) two variables, for instance f(x,y) = sin(x^2+y^2)/(x^2+y^2).

I would use it like this (pseudo code):
FuncTree := BuildEvalTree('f(x,y) = sin(x^2+y^2)/(x^2+y^2)'); // Or whatever it needs
for x := x_min to x_max do
for y := y_min to y_max do
z[x,y] := Evaluate(FuncTree,[x,y]); // Or whatever it needs...

Thanks!

138 comments:

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    ReplyDelete
  2. I use a free unit called MathExpression written by Alex Demchenko (alex@ritlabs.com) that I downloaded years ago from http://www.cobans.net. The unit doesn't seem to be on his site any more but it is used in our software extensively for evaluating mathematical expressions. It includes sin, cos, sqrt, etc.

    ReplyDelete
  3. @Fritz: Thanks. I saw that one, but it builds assembly at run-time, so it won't work on 64-bit or ARM (iOS). I will however, shoot Hallvard a message. :)

    @Jason: I'll look for it. Do you mind sending it over (assuming that doesn't violate anything)? I will contact Alex as well. Thanks!

    ReplyDelete
  4. @Jason: Found it! http://www.torry.net/authorsmore.php?id=3749

    ReplyDelete
  5. @Jason: MathExpression only handles functions of one variable (y=f(x)), not two (z=f(x,y)). Any chance you've modified it to handle more than one already?

    ReplyDelete
  6. How about TExpressionParser: http://www.delphipages.com/comp/texpressionparser-3389.html

    ReplyDelete
  7. cyMathParser in Cindy Components (sourceforge)!

    ReplyDelete
  8. Take a look at the TESBExpressEdit and TESBExprEvaluator in Glenn Crouch's ESBPCS for VCL components. If you don't want the full set of components, these components are available in the Calcs and Lite subsets. The expression evaluator handles up to 10 variables, allowing expressions to contain arithmetic (with full precedence), brackets, trigonometry, hyperbolics, powers, logarithms and other functions. Glenn hasn't charged for upgrades/updates since I bought his components for D6. I have no business relationship to Glenn except as a satisfied user.

    http://www.esbconsult.com/esbpcs/ESBPCSExprEvaluator.htm

    ReplyDelete
  9. You could use Barry Kelly's expression evaluator in the JCL.

    program JclExprTestAO;

    {$APPTYPE CONSOLE}

    uses
    SysUtils, JclExprEval, JclMath;

    procedure Test;
    var
    CE: TCompiledEvaluator;
    FX, FY: Double;
    X, Y: Integer;
    Z: array [1..19, 1..19] of Double;
    begin
    CE := TCompiledEvaluator.Create;
    try
    CE.AddFunc('Sin', Sin);
    CE.AddVar('x', FX);
    CE.AddVar('y', FY);
    CE.Compile('sin(x*x+y*y)/(x*x+y*y)');
    for X := Low(Z) to High(Z) do
    for Y := Low(Z[X]) to High(Z[X]) do
    begin
    FX := X;
    FY := Y;
    Z[X, Y] := CE.Evaluate;
    end;
    finally
    CE.Free;
    end;
    end;

    begin
    try
    Test;
    except
    on E: Exception do
    begin
    Writeln('Exception Error');
    WriteLn(' ClassName=', E.ClassName);
    WriteLn(' Message=', E.Message);
    end;
    end;
    end.

    ReplyDelete
  10. Well the JCL is supposed to work with FPC, but it doesn't compile out of the box for OSX32 and don't think it will for FPC ARM. However I guess it doesn't take that much to get JclExprEval compiling after replacing some dependencies.

    ReplyDelete
  11. The JCL one looks interesting... What does Compile do? Machine code? Or build an expression evaluation tree that's used for each eval later?

    I have MathExpression up and running for functions of two variables. I does OK with 50,000 points on a desktop - takes about 2 seconds. On the iPad 3 however, it takes close to a minute... So I need something that doesn't parse the function every single call. It should just evaluate an existing tree.

    ReplyDelete
  12. It compiles to an expression tree. The following loop with your expression takes about one second on my very old Core2 system.

    for I := 0 to 999999 do
    Z[1, 1] := CE.Evaluate;

    Doing the same with TEvaluator takes about twelve seconds.

    Our help says this about TCompiledEvaluator

    Summary:
    An evaluator that first compiles an expression into an
    intermediate form, then evaluates it on demand.
    Description:
    This evaluator is suitable for applications like graphing, where
    there is just one expression which is constantly evaluated with
    variables and/or functions changing value. It takes longer to
    compile than TEvaluator does to evaluate, but once compiled is
    much faster.

    ReplyDelete
  13. I have just one such thing handy, built by myself. It does most of the functions that Delphi brings, parses into a tree, precomputes constant parts, and can handle variables (and constants) with names of your choice, does proper operator precedence and brackets, and even logical operators. And it does not contain any assembly, nor does it create any. Sounds pretty much like your thing, except that it does not handle the "f(x, y)=" part, but as long as that stays fixed, it can be evaluated in a double loop like the JCL one.
    It even is reasonably fast, but I haven't tested it on any other machine besides Windows based boxes. But since it's all straight forward pascal without dirty hacks, it should do well.

    Downside: I currently have it at work only, so if you're interested, please drop me a note via e-mail. That way I will remember that I wanted to send you the file on Monday when the wine wears off :)

    ReplyDelete
  14. @Uwe: Sounds great! I must try! :)

    @Medium: Sure, I'll try it out too. I don't have your email address though... :(

    ReplyDelete
  15. Oops, I thought you as blog owner would see it.
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    ReplyDelete
  16. Uwe, I just did the minimum required files for your example as a Win32 app...

    crossplatform.inc
    jcl.inc
    Jcl8087.pas
    JclAnsiStrings.pas
    JclBase.pas
    JclCharsets.pas
    JclConsole.pas
    jcld16win32.inc
    JclDateTime.pas
    JclExprEval.pas
    JclFileUtils.pas
    JclIniFiles.pas
    JclLogic.pas
    JclMath.pas
    JclRegistry.pas
    JclResources.pas
    JclSecurity.pas
    JclShell.pas
    JclStreams.pas
    JclStrHashMap.pas
    JclStringConversions.pas
    JclStrings.pas
    JclSynch.pas
    JclSysInfo.pas
    JclSysUtils.pas
    JclUnicode.pas
    JclUnicode.res
    JclWideStrings.pas
    JclWin32.pas
    jedi.inc
    Snmp.pas
    windowsonly.inc

    That's a lot to port for OSX and iOS...

    It is *fast* though... ;)

    ReplyDelete
  17. @Alan: Thanks! TExpressionParser is *exactly* what I needed. Small, effecient and portable. I only had to port a few lines to get it onto iOS. There's virtually no difference in execution speed on my iPhone 4 with 50,000 points calculated and plotted. Renders very fast! Awesome!

    ReplyDelete
  18. Great that you've a solution!

    A little disadvantage of bigger libraries is that the usage of a class or functions needs a lot code to compile too that is actually not used by the class or function. I've started with JclExprEval and added to the used units only the stuff that is actually used and ended up with the following files:
    jcl.inc
    jedi.inc
    jcld16.inc
    JclBase.pas
    JclExprEval.pas
    JclResources.pas
    JclStrHashMap.pas
    JclStrings.pas
    JclSysUtils.pas

    It worked then with no changes for OSX32 and for FPC ARM Linux (Android) I had to implement the minimum required pieces of LoadCharTypes and LoadCaseMap in JclStrings.pas to make the evaluator work.

    ReplyDelete
  19. Thanks Uwe (and all)! Keep up the great work!

    ReplyDelete
  20. - FatExpression Parser maybe a good election also, Don't know how faster can be but it is flexible because you can add custom functions and also support for string functions.

    There are many free versions of these component, you can also find it at Torry's site.


    - Take a look at TArtFormula package
    http://artsoft.nm.ru/works.html#formula
    It seems also quite good.

    ReplyDelete
  21. @Anders, @Alan
    Found a newer (2002!) version of TExpressionParser, on the author's website: http://www.aew.wur.nl/UK/TExpressionParser/

    ReplyDelete
  22. ArtFormula compiles for win32 and winCE for ARM BUT winCE for ARM returns incorrect results... so test your equations.

    ReplyDelete
  23. bestcode.com has a TbcParser which is a math expression component for Delphi. You can define custom variables and functions. It runs fast.

    ReplyDelete
  24. TbcParser works great: http://www.bestcode.com/html/math_parser_for_delphi.html

    ReplyDelete
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  33. Thanks for posting the link. I just got TbcParser and verified it works on iPhone and MacOSX too!

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  43. I have downloadable Mathematical Expression Parsers in Java and C++ over here:

    http://www.technical-recipes.com/2011/a-mathematical-expression-parser-in-java-and-cpp/

    Both implement the shunting yard algorithm to convert your expression into reverse Polish notation and then evaluate the resuly.

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