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c# - Best algorithm for evaluating a mathematical expression?

What's the best algorithm for evaluating a mathematical expression? I'd like to be able to optimize this a little in the sense that I may have one formula with various variables, which I may need to evaluate hundreds of times using different variables. So basically if I can initially parse the formula so that it is optimized in some way, and I can then pass in the variables to this optimized version as many times as I need, each time it produces a result for me.

I'll be writing this in either Delphi or C#. I have already written something similar by using the shunting yard algorithm, but each time I need to calculate the same formula, I'm having to go through the parsing stage. There must be a better way to do this.

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If you want to do it with Delphi, you could look into how the JclExprEval unit works, part of the JEDI Code Library. I wrote it several years ago (it's a little over-engineered); it parses functions and variables and can hand you back a method pointer which evaluates the expression quickly. Pass the variables in by reference, and you can change them directly and the re-evaluated expression will be calculated accordingly.

In any case, the basics of how it works may be helpful for you. Recursive-descent parsing of expressions is easy, and by building a tree you can evaluate multiple times without re-parsing. JclExprEval actually generates code for a simple stack machine, so that it can work a little faster than tree interpretation; stack machines largely restrict their memory operations to arrays and use switches for opcodes, while tree interpretation follows links throughout the heap and often uses virtual dispatch (or double-dispatch) for opcodes, so they usually end up slower.

Taking the same approach as JclExprEval in parsing but written in C#, and building up an Expression, like Marc suggests, is another perfectly valid approach. The JIT-compiled expression ought to be quite a bit faster than an interpreted expression program or tree, which themselves are a lot faster than parsing.


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