What's the best way to read a mathematical function f(x,y) command line argument?

Question

From main() , I want the user to input a mathematical function (I,e: 2xy) through the command line. From there, I initially thought to iterate through the string and parse out different arithmetic operators, x, y, etc. However, this could become fairly complicated for more intricate functions, (eg: (2x^2)/5 +sqrt(x^4) ). Is there a more general method to be able to parse a mathematical function string like this one?

Answer 1

One of the most helpful ways to deal with parsing issues like that is to switch the input methods from equations like that to an RPN based input where the arguments come first and the operators come last.

Rewriting your complex equation would end up looking like:

2 2 x ^ * 5 / x 4 ^ sqrt +

This is generally easier to implement, as you can do it with a simple stack -- pushing new arguments on, while the operators pull the require pieces off the stack and put the result back on. Greatly simplifies the parsing, but you still need to implement the functions.

Answer 2

What you need is an expression evaluator .

A while ago, I wrote a complete C expression evaluator (ie evaluated expressions written using C syntax) for a command line processor and scripting language on an embedded system. I used this description of the algorithm as a starting point. You could use the accompanying code directly, but I did not like the implementation, and wrote my own from the algorithm description.

It needed some work to support all C operators, function calls, and variables, but is a clear explanation and therefore a good starting point, especially if you don't need that level of completeness.

The basic principle is that expression evaluation is easier for a computer using a stack and 'Reverse Polish Notation', so the algorithm converts an in-fix notation expression with associated order of precedence and parentheses to RPN, and then evaluates it by popping operands, performing operations, and pushing results, until there are no operations left and one value left on the stack.

It might get a bit more complicated is you choose to deal with implicit multiply operators ( 2xy rather then 2 * x * y for example. Not least because you'd need to unambiguously distinguish the variables x and y from a single variable xy . That is probably only feasible if you only allow single character variable names. I suggest you either do that and insert explicit multiply operators on the operator stack as part of the parse, or you disallow implicit multiply.