I want to write a program that takes an string like x^2+1 and understand it.
I want to ask the user to enter her/his function and I want to be able to process and understand it. Any Ideas?
char s[100];
s <- "x*I+2"
x=5;
I=2;
res=calc(s);
I think it could be done by something like string analyses but I think Its so hard for me.
I have another Idea and that is using tcc in main program and doing a realtime compile and run and delete a seprated program (or maybe function) that has the string s in it.
and I will create a temp file every time and ask tcc to compile it and run it by exec or similar syntax.
/*tmp.cpp:*/
#include <math.h>
void main(/*input args*/){
return x*I+2;
}
the tmp.cpp will created dynamically.
thanks in advance.
I am not sure what do you expect. It's too complex to give the code as answer, but the general idea is not very complex. It's not out of reach to code, even for a normal hobbyist programmer.
You need to define grammar, tokenize string, recognize operators, constants and variables.
Probably put expression into a tree. Make up a method for substituting the variables... and you can evaluate!
You need to have some kind of a parser. The easiest way to have math operations parsable is to have them written in RPN. You can, however, write your own parser using parser libraries, like Spirit from boost or Yacc
I use with success , function parser
from www it looks like it supports also std::complex, but I never used it
As luck would have it, I recently wrote one!
Look for {,include/}lib/MathExpression/Term. It handles complex numbers but you can easily adapt it for plain old floats.
The licence is GPL 2.
The theory in brief, when you have an expression like
X*(X+2)
Your highest level parser can parse expressions of the form A + B + C... In this case A is the whole expression.
You recurse to parse an operator of higher precedence, A * B * C... In this case A is X and B is (X+2)
Keep recursing until you're parsing either basic tokens such as X or hit an opening parenthesis, in which case push some kind of stack to track where your are and recurse into the parentheses with the top-level low-precedence parser.
I recommend you use RAII and throw exceptions when there are parse errors.
use a Recursive descent parser
Sample: it's in german, but a small and powerfull solution
look here
here is exactly what You are searching for. Change the function read_varname to detect a variable like 'x' or 'I'.
Related
So I have this maths project where I have to write a program which calculates definite integral of a given function within the given boundaries. I've done this using C++ and CodeBlocks, but now I would like to try and make it possible to input function using cmd when I run my code in CodeBlocks, just like I input boundaries, so I don't have to edit this line of code every time I want to run it for different function. I realised that this would require actually using then this input ( e.g. "sqrt(pow(x,2)-1)" ) as part of the code when entered, and I really don't know how to do this or if it is possible at all, so any help is welcome.
This the part of the code which handles function:
double Formula(double x)
{
double a;
a = sqrt(x);
return a;
}
If you want to evaluate expression like "sqrt(pow(x,2)-1)", you have to:
parse the string and generate an AST (Abstract syntax tree) which describes the operations to execute
use an evaluation function on the AST
For example, if you have "sqrt(pow(x,2)-1)" in input, the AST could be represented like this:
function - sqrt
function - substract
function - pow
variable - x
integer - 2
integer - -1
You have to define the structures which will be used to represent your AST.
Then, to parse the query string you have 2 choices:
parse it yourself, count the parentheses etc...
use a tool to generate the parser: yacc + lex or under linux bison + flex. These tools require time to be used to them.
If you have just a little project to do, you may have to try to parse the input yourself to generate the AST.
If the project is a compilation project, you should use bison + flex, they are exactly made for that (but require time to be used to ! ).
Alternatively, integrate with a scripting language, make it do the function parsing and evaluation. It will be considerably slower though.
JavaScript interpreters are all over the place. Python is fairly popular, too. Some people like Lua.
(EDITED both title and main text and created a spin-off question that arose)
For our application it would be ideal to parse a simple DSL of logical expressions. However the way I'd like to do this is to parse (at runtime) the input text which gives the expressions into some lazily evaluated structure (an expression template) which can then be later used within more performance sensitive code.
Ideally the evaluation is as fast as possible using this technique as it will be used a large number of times with different values substituting into the placeholders each time. I'm not expecting the expression template to be equivalent in performance to say a hardcoded function that models the same function as the given input text string i.e. there is no need to go down a route of actually compiling say, c++, in situ of a running program (I believe other questions cover dynamic library compiling/loading).
My own thoughts reading examples from boost is that I can use boost::spirit to do the parsing of the input text and I'm confident I can develop the grammar I need. However, I'm not sure how I can combine the parser with boost::proto to build an executable expression template. Most examples of spirit that I've seen are merely interpreters or end up building some kind of syntax tree but go no further. Most examples of proto that I've seen assume the DSL is embedded in the host source code and does not need to be initially interpreted from a string. I'm aware that boost::spirit is actually implemented with boost::proto but not sure if this is relevant to the problem or whether that fact will suggest a convenient solution.
To re-iterate, I need to be able to make real the something like following:
const std::string input_text("a && b || c");
// const std::string input_text(get_dsl_string_from_file("expression1.dsl"));
Expression expr(input_text);
while(keep_intensively_processing) {
...
Context context(…);
// e.g. context.a = false; context.b=false; context.c=true;
bool result(evaluate(expr, context));
...
}
I would really appreciate a minimal example or even just a small kernel that I can build upon that creates an expression from input text which is evaluated later in context.
I don't think this is exactly the same question as posted here: parsing boolean expressions with boost spirit
as I'm not convinced this is necessarily the quickest executing way of doing this, even though it looks very clever. In time I'll try to do a benchmark of all answers posted.
As the topic indicates, my program needs to read several function expressions and plug-in different variables many times. Parsing the whole expression again every time I need to plug-in a new value is definitely way too ugly, so I need a way to store parsed expression.
The expression may look like 2x + sin(tan(5x)) + x^2. Oh, and the very important point -- I'm using C++.
Currently I have three ideas on it, but all not very elegant:
Storing the S-expression as a tree; evaluate it by recurring. It may
be the old-school way to handle this, but it's ugly, and I would
have to handle with different number of parameters (like + vs. sin).
Composing anonymous functions with boost::lambda. It may work nice,
but personally I don't like boost.
Writing a small python/lisp script, use its native lambda
expression and call it with IPC... Well, this is crazy.
So, any ideas?
UPDATE:
I did not try to implement support for parenthesis and functions with only one parameter, like sin().
I tried the second way first; but I did not use boost::lambda, but a feature of gcc which could be used to create (fake) anonymous functions I found from here. The resulting code has 340 lines, and not working correctly because of scoping and a subtle issue with stack.
Using lambda could not make it better; and I don't know if it could handle with scoping correctly. So sorry for not testing boost::lambda.
Storing the parsed string as S-expressions would definitely work, but the implementation would be even longer -- maybe ~500 lines? My project is not that kind of gigantic projects with tens of thousands lines of code, so devoting so much energy on maintaining that kind of twisted code which would not be used very often seems not a nice idea.
So finally I tried the third method -- it's awesome! The Python script has only 50 lines, pretty neat and easy to read. But, on the other hand, it would also make python a prerequisite of my program. It's not that bad on *nix machines, but on windows... I guess it would be very painful for the non-programmers to install Python. So is lisp.
However, my final solution is opening bc as a subprocess. Maybe it's a bad choice for most situations, however, it fits me well.
On the other hand, for projects work only under *nix or already have python as a prerequisite, personally I recommend the third way if the expression is simple enough to be parsed with hand-written parser. If it's very complicated, like Hurkyl said, you could consider creating a mini-language.
Why not use a scripting language designed for exactly this kind of purpose? There are several such languages floating around, but my experience is with lua.
I use lua to do this kind of thing "all the time". The code to embed and parse an expression like that is very small. It would look something like this (untested):
std::string my_expression = "2*x + math.sin( math.tan( x ) ) + x * x";
//Initialise lua and load the basic math library.
lua_State * L = lua_open();
lua_openmath(L);
//Create your function and load it into lua
std::string fn = "function myfunction(x) return "+my_expression+"end";
luaL_dostring( L, fn.c_str(), fn.size() );
//Use your function
for(int i=0; i<10; ++i)
{
// add the function to the stack
lua_getfield(L, LUA_GLOBALSINDEX, "myfunction");
// add the argument to the stack
lua_pushnumber(L, i);
// Make the call, using one argument and expecting one result.
// stack looks like this : FN ARG
lua_pcall(L,1,1)
// stack looks like this now : RESULT
// so get the result and print it
double result = lua_getnumber(L,-1);
std::cout<<i<<" : "<<result<<std::endl;
// The result is still on the stack, so clean it up.
lua_pop(L,1);
}
I'm writing some excel-like C++ console app for homework.
My app should be able to accept formulas for it's cells, for example it should evaluate something like this:
Sum(tablename\fieldname[recordnumber], fieldname[recordnumber], ...)
tablename\fieldname[recordnumber] points to a cell in another table,
fieldname[recordnumber] points to a cell in current table
or
Sin(fieldname[recordnumber])
or
anotherfieldname[recordnumber]
or
"10" // (simply a number)
something like that.
functions are Sum, Ave, Sin, Cos, Tan, Cot, Mul, Div, Pow, Log (10), Ln, Mod
It's pathetic, I know, but it's my homework :'(
So does anyone know a trick to evaluate something like this?
Ok, nice homework question by the way.
It really depends on how heavy you want this to be. You can create a full expression parser (which is fun but also time consuming).
In order to do that, you need to describe the full grammar and write a frontend (have a look at lex and yacc or flexx and bison.
But as I see your question you can limit yourself to three subcases:
a simple value
a lookup (possibly to an other table)
a function which inputs are lookups
I think a little OO design can helps you out here.
I'm not sure if you have to deal with real time refresh and circular dependency checks. Else they can be tricky too.
For the parsing, I'd look at Recursive descent parsing. Then have a table that maps all possible function names to function pointers:
struct FunctionTableEntry {
string name;
double (*f)(double);
};
You should write a parser. Parser should take the expression i.e., each line and should identify the command and construct the parse tree. This is the first phase. In the second phase you can evaluate the tree by substituting the data for each elements of the command.
Previous responders have hit it on the head: you need to parse the cell contents, and interpret them.
StackOverflow already has a whole slew of questions on building compilers and interperters where you can find pointers to resources. Some of them are:
Learning to write a compiler (#1669 people!)
Learning Resources on Parsers, Interpreters, and Compilers
What are good resources on compilation?
References Needed for Implementing an Interpreter in C/C++
...
and so on.
Aside: I never have the energy to link them all together, or even try to build a comprehensive list.
I guess you cannot use yacc/lex (or the like) so you have to parse "manually":
Iterate over the string and divide it into its parts. What a part is depends on you grammar (syntax). That way you can find the function names and the parameters. The difficulty of this depends on the complexity of your syntax.
Maybe you should read a bit about lexical analysis.
We would like to have user defined formulas in our c++ program.
e.g. The value v = x + ( y - (z - 2)) / 2. Later in the program the user would define x,y and z -> the program should return the result of the calculation. Somewhen later the formula may get changed, so the next time the program should parse the formula and add the new values. Any ideas / hints how to do something like this ? So far I just came to the solution to write a parser to calculate these formulas - maybe any ideas about that ?
If it will be used frequently and if it will be extended in the future, I would almost recommend adding either Python or Lua into your code. Lua is a very lightweight scripting language which you can hook into and provide new functions, operators etc. If you want to do more robust and complicated things, use Python instead.
You can represent your formula as a tree of operations and sub-expressions. You may want to define types or constants for Operation types and Variables.
You can then easily enough write a method that recurses through the tree, applying the appropriate operations to whatever values you pass in.
Building your own parser for this should be a straight-forward operation:
) convert the equation from infix to postfix notation (a typical compsci assignment) (I'd use a stack)
) wait to get the values you want
) pop the stack of infix items, dropping the value for the variable in where needed
) display results
Using Spirit (for example) to parse (and the 'semantic actions' it provides to construct an expression tree that you can then manipulate, e.g., evaluate) seems like quite a simple solution. You can find a grammar for arithmetic expressions there for example, if needed... (it's quite simple to come up with your own).
Note: Spirit is very simple to learn, and quite adapted for such tasks.
There's generally two ways of doing it, with three possible implementations:
as you've touched on yourself, a library to evaluate formulas
compiling the formula into code
The second option here is usually done either by compiling something that can be loaded in as a kind of plugin, or it can be compiled into a separate program that is then invoked and produces the necessary output.
For C++ I would guess that a library for evaluation would probably exist somewhere so that's where I would start.
If you want to write your own, search for "formal automata" and/or "finite state machine grammar"
In general what you will do is parse the string, pushing characters on a stack as you go. Then start popping the characters off and perform tasks based on what is popped. It's easier to code if you force equations to reverse-polish notation.
To make your life easier, I think getting this kind of input is best done through a GUI where users are restricted in what they can type in.
If you plan on doing it from the command line (that is the impression I get from your post), then you should probably define a strict set of allowable inputs (e.g. only single letter variables, no whitespace, and only certain mathematical symbols: ()+-*/ etc.).
Then, you will need to:
Read in the input char array
Parse it in order to build up a list of variables and actions
Carry out those actions - in BOMDAS order
With ANTLR you can create a parser/compiler that will interpret the user input, then execute the calculations using the Visitor pattern. A good example is here, but it is in C#. You should be able to adapt it quickly to your needs and remain using C++ as your development platform.