用于评估数学表达式的最佳算法？ [英] Best algorithm for evaluating a mathematical expression?
问题描述
评估数学表达式的最佳算法是什么？我想能够优化这一点，因为我可能有一个公式与各种变量，我可能需要评估数百次使用不同的变量。所以基本上，如果我可以初始解析公式，以便以某种方式进行优化，然后我可以将变量传递给这个优化版本，因为我需要多次，每次为我生成一个结果。
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.
我将在Delphi或C＃中编写。我已经通过使用分流场算法编写了类似的东西，但是每当我需要计算相同的公式时，我必须经过解析阶段。必须有一个更好的方式来做到这一点。
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.
推荐答案
如果要使用Delphi进行操作，可以查看 JclExprEval 单元作品，是 JEDI代码库的一部分。几年前我写了（这有点过度设计）;它解析函数和变量，并且可以回传一个快速评估表达式的方法指针。通过引用传递变量，您可以直接更改它们，并相应地计算重新计算的表达式。
If you want to do it with Delp 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.
无论如何，它的基本原理如何对你有帮助表达式的递归下降解析很容易，通过构建树可以多次评估，无需重新解析。 JclExprEval实际上为一个简单的堆栈机器生成代码，因此它可以比树解释更快一些;堆栈机器很大程度上将其内存操作限制为阵列，并使用开关作为操作码，而树解释则遵循整个堆中的链接，并且经常使用虚拟调度（或双调度）作为操作码，因此通常会更慢。
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.
采用与code> JclExprEval 相同的方法，但在C＃中编写，并构建一个 Expression 是另一个完全有效的方法。 JIT编译的表达式应该比解释表达式程序或树更快一些，它们本身比解析快很多。
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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